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CANONICAL BUNDLE

  • Canonical bundle
  • Concept in algebraic geometry

    the canonical bundle of a non-singular algebraic variety V {\displaystyle V} of dimension n {\displaystyle n} over a field is the line bundle Ω n =

    Canonical bundle

    Canonical_bundle

  • Riemann–Roch theorem
  • Relation between genus, degree, and dimension of function spaces over surfaces

    denoted h 0 ( X , L ) {\displaystyle h^{0}(X,L)} . Let K denote the canonical bundle on X. Then, the Riemann–Roch theorem states that h 0 ( X , L ) − h

    Riemann–Roch theorem

    Riemann–Roch_theorem

  • Elliptic surface
  • Mathematical concept

    compute the canonical bundle of a minimal elliptic surface f: X → S. Over the complex numbers, Kodaira proved the following canonical bundle formula: K

    Elliptic surface

    Elliptic_surface

  • Tautological bundle
  • Vector bundle existing over a Grassmannian

    also tautological bundles on a projective bundle of a vector bundle, as well as a Grassmann bundle. The older term canonical bundle has dropped out of

    Tautological bundle

    Tautological_bundle

  • Generalized complex structure
  • Property of a differential manifold that includes complex structures

    the canonical bundle in the ordinary case. It is sometimes also called the pure spinor bundle, as its sections are pure spinors. The canonical bundle is

    Generalized complex structure

    Generalized_complex_structure

  • Canonical coordinates
  • Sets of coordinates on phase space which can be used to describe a physical system

    of canonical coordinates in classical mechanics may be generalized to a more abstract 20th century definition of coordinates on the cotangent bundle of

    Canonical coordinates

    Canonical_coordinates

  • Calabi–Yau manifold
  • Riemannian manifold with SU(n) holonomy

    power of the canonical bundle of M {\displaystyle M} is trivial. M {\displaystyle M} has a finite cover that has trivial canonical bundle. M {\displaystyle

    Calabi–Yau manifold

    Calabi–Yau manifold

    Calabi–Yau_manifold

  • Tangent bundle
  • Tangent spaces of a manifold

    the canonical projection. Pushforward (differential) Unit tangent bundle Cotangent bundle Frame bundle Musical isomorphism Holomorphic tangent bundle The

    Tangent bundle

    Tangent bundle

    Tangent_bundle

  • Coherent sheaf
  • Generalization of vector bundles

    , the canonical bundle K X {\displaystyle K_{X}} means the line bundle Ω n {\displaystyle \Omega ^{n}} . Thus sections of the canonical bundle are algebro-geometric

    Coherent sheaf

    Coherent_sheaf

  • Canonical
  • Standard or referential form

    element of a set partition Canonical one-form, a special 1-form defined on the cotangent bundle T*M of a manifold M Canonical symplectic form, the exterior

    Canonical

    Canonical

  • Gorenstein scheme
  • Algebraic geometry scheme

    locally Noetherian scheme whose local rings are all Gorenstein. The canonical line bundle is defined for any Gorenstein scheme over a field, and its properties

    Gorenstein scheme

    Gorenstein_scheme

  • Canonical ring
  • ) {\displaystyle R(V,K)=R(V,K_{V})\,} of sections of powers of the canonical bundle K. Its nth graded component (for n ≥ 0 {\displaystyle n\geq 0} ) is:

    Canonical ring

    Canonical_ring

  • Vector bundle
  • Mathematical parametrization of vector spaces by another space

    vector bundle E* is the Hom bundle Hom(E, R × X) of bundle homomorphisms of E and the trivial bundle R × X. There is a canonical vector bundle isomorphism

    Vector bundle

    Vector bundle

    Vector_bundle

  • Adjunction formula
  • Concept in algebraic geometry

    the theory of complex manifolds, the adjunction formula relates the canonical bundle of a variety and a hypersurface inside that variety. It is often used

    Adjunction formula

    Adjunction_formula

  • K3 surface
  • Type of smooth complex surface of kodaira dimension 0

    a compact connected complex manifold of dimension 2 with а trivial canonical bundle and irregularity zero. An (algebraic) K3 surface over any field means

    K3 surface

    K3 surface

    K3_surface

  • Cotangent bundle
  • Vector bundle of cotangent spaces at every point in a manifold

    cotangent bundle can be understood to be a phase space on which Hamiltonian mechanics plays out. The cotangent bundle carries a canonical one-form θ

    Cotangent bundle

    Cotangent_bundle

  • Higgs bundle
  • Type of vector bundle

    (L)\subset L\otimes K} with K {\displaystyle K} the canonical bundle over the Riemann surface M. Then a Higgs bundle ( E , φ ) {\displaystyle (E,\varphi )} is stable

    Higgs bundle

    Higgs_bundle

  • Ample line bundle
  • Concept in algebraic geometry

    variety whose canonical bundle is anti-ample Matsusaka's big theorem Divisorial scheme: a scheme admitting an ample family of line bundles Holomorphic vector

    Ample line bundle

    Ample_line_bundle

  • Kodaira dimension
  • Concept in algebraic geometry

    dimensional varieties (under the name of canonical dimension), and later named it after Kunihiko Kodaira. The canonical bundle of a smooth algebraic variety X

    Kodaira dimension

    Kodaira_dimension

  • Kähler–Einstein metric
  • Type of metric in Riemannian geometry

    in terms of the canonical bundle of X {\displaystyle X} : c 1 ( X ) < 0 {\displaystyle c_{1}(X)<0} if and only if the canonical bundle K X {\displaystyle

    Kähler–Einstein metric

    Kähler–Einstein_metric

  • Euler sequence
  • Short exact sequence of sheaves on projective space

    projective spaces are Fano varieties, because the canonical bundle is anti-ample and this line bundle has no non-zero global sections, so the geometric

    Euler sequence

    Euler_sequence

  • Canonical form
  • Standard representation of a mathematical object

    cotangent bundle. That bundle can always be endowed with a certain differential form, called the canonical one-form. This form gives the cotangent bundle the

    Canonical form

    Canonical form

    Canonical_form

  • Dualizing module
  • dualizing module, also called a canonical module, is a module over a commutative ring that is analogous to the canonical bundle of a smooth variety. It is

    Dualizing module

    Dualizing_module

  • Ricci curvature
  • Tensor in differential geometry

    determines the curvature form of the canonical line bundle. The canonical line bundle is the top exterior power of the bundle of holomorphic Kähler differentials:

    Ricci curvature

    Ricci curvature

    Ricci_curvature

  • Theta characteristic
  • the canonical class. In terms of holomorphic line bundles L on a connected compact Riemann surface, it is therefore L such that L2 is the canonical bundle

    Theta characteristic

    Theta_characteristic

  • Surface of general type
  • Castelnuovo surfaces: Another extremal case, Castelnuovo proved that if the canonical bundle is very ample for a surface of general type then c 1 2 ⩾ 3 p g − 7

    Surface of general type

    Surface_of_general_type

  • Kähler manifold
  • Manifold with Riemannian, complex and symplectic structure

    the tangent bundle of X {\displaystyle X} in H 2 ( X , R ) {\displaystyle H^{2}(X,\mathbb {R} )} . It follows that the canonical bundle of a compact

    Kähler manifold

    Kähler_manifold

  • Canonical singularity
  • Singularities of algebraic varieties

    When X is a smooth variety of dimension n over a field k, its canonical line bundle is defined as the sheaf of n-forms (or "volume forms") on X, ω X

    Canonical singularity

    Canonical_singularity

  • Serre duality
  • Theorem in algebraic geometry

    Define the canonical line bundle K X {\displaystyle K_{X}} to be the bundle of n-forms on X, the top exterior power of the cotangent bundle: K X = Ω X

    Serre duality

    Serre_duality

  • Gorenstein ring
  • Local ring in commutative algebra

    simply a line bundle (viewed as a complex in degree −dim(X)); this line bundle is called the canonical bundle of X. Using the canonical bundle, Serre duality

    Gorenstein ring

    Gorenstein_ring

  • Hitchin system
  • Type of integrable system

    cotangent bundle to the moduli space of stable G-bundles for some reductive group G, on some compact algebraic curve. This space is endowed with a canonical symplectic

    Hitchin system

    Hitchin_system

  • Birational geometry
  • Field of algebraic geometry

    modern definition is that a projective variety X is minimal if the canonical line bundle KX has nonnegative degree on every curve in X; in other words, KX

    Birational geometry

    Birational geometry

    Birational_geometry

  • Iitaka dimension
  • its canonical bundle is big, but the rational map it determines is not a birational isomorphism. Instead, it is a two-to-one cover of the canonical curve

    Iitaka dimension

    Iitaka_dimension

  • Tautological one-form
  • Canonical differential form

    Poincaré one-form, the canonical one-form, or the symplectic potential. A similar object is the canonical vector field on the tangent bundle. To define the tautological

    Tautological one-form

    Tautological_one-form

  • Semiorthogonal decomposition
  • "indecomposable". In particular, for a smooth projective variety X whose canonical bundle K X {\displaystyle K_{X}} is basepoint-free, every semiorthogonal decomposition

    Semiorthogonal decomposition

    Semiorthogonal_decomposition

  • Modular form
  • Analytic function on the upper half-plane with a certain behavior under the modular group

    square of the Hodge bundle is identified with the logarithmic canonical bundle of the modular curve, i.e., the canonical bundle twisted with the cuspidal

    Modular form

    Modular_form

  • Canonical map
  • Mathematical mapping between objects arising from their definitions

    If E is a vector bundle over a topological space X, then the projection map from E to X is the structure map. In topology, a canonical map is a function

    Canonical map

    Canonical_map

  • Abundance conjecture
  • log terminal singularities over a field k {\displaystyle k} if the canonical bundle K X {\displaystyle K_{X}} is nef, then K X {\displaystyle K_{X}} is

    Abundance conjecture

    Abundance_conjecture

  • Double tangent bundle
  • double tangent bundle or the second tangent bundle refers to the tangent bundle (TTM,πTTM,TM) of the total space TM of the tangent bundle (TM,πTM,M) of

    Double tangent bundle

    Double_tangent_bundle

  • Complex geometry
  • Study of complex manifolds and several complex variables

    Calabi–Yau manifolds. These are given by Kähler manifolds with trivial canonical bundle K X = Λ n T 1 , 0 ∗ X {\displaystyle K_{X}=\Lambda ^{n}T_{1,0}^{*}X}

    Complex geometry

    Complex_geometry

  • Geometric quantization
  • Recipe for constructing a quantum analog of a classical physical theory

    The line bundle L {\displaystyle L} is replaced by the tensor product of L {\displaystyle L} with the square root of the canonical bundle of the polarization

    Geometric quantization

    Geometric_quantization

  • Gauge theory (mathematics)
  • Study of vector bundles, principal bundles, and fibre bundles

    theory is the general study of connections on vector bundles, principal bundles, and fibre bundles. Gauge theory in mathematics should not be confused

    Gauge theory (mathematics)

    Gauge_theory_(mathematics)

  • Grothendieck–Riemann–Roch theorem
  • Result in algebraic geometry

    complexes of coherent sheaves is canonically isomorphic to the Grothendieck group of bounded complexes of finite-rank vector bundles. Using this isomorphism,

    Grothendieck–Riemann–Roch theorem

    Grothendieck–Riemann–Roch theorem

    Grothendieck–Riemann–Roch_theorem

  • Castelnuovo surface
  • type such that the canonical bundle is very ample and such that c12 = 3pg − 7. Guido Castelnuovo proved that if the canonical bundle is very ample for

    Castelnuovo surface

    Castelnuovo_surface

  • Quintic threefold
  • 3d hypersurface of degree 5

    {\displaystyle \mathbb {C} } . Then using the adjunction formula to compute its canonical bundle, we have Ω X 3 = ω X = ω P 4 ⊗ O ( d ) ≅ O ( − ( 4 + 1 ) ) ⊗ O ( d

    Quintic threefold

    Quintic_threefold

  • List of unsolved problems in mathematics
  • eventually periodic? Rendezvous problem Abundance conjecture: if the canonical bundle of a projective variety with Kawamata log terminal singularities is

    List of unsolved problems in mathematics

    List_of_unsolved_problems_in_mathematics

  • Nagata's conjecture on curves
  • Mathematical proposition

    cases r > 9 and r ≤ 9 are distinguished by whether or not the anti-canonical bundle on the blowup of P2 at a collection of r points is nef. In the case

    Nagata's conjecture on curves

    Nagata's_conjecture_on_curves

  • Principal bundle
  • Fiber bundle whose fibers are group torsors

    ordered basis of a vector space, a frame bundle lacks a canonical choice of identity cross-section. Principal bundles have important applications in topology

    Principal bundle

    Principal_bundle

  • Enriques–Kodaira classification
  • Mathematical classification of surfaces

    plurigenera and the Hodge numbers defined as follows: K is the canonical line bundle whose sections are the holomorphic 2-forms. P n = dim ⁡ H 0 ( K

    Enriques–Kodaira classification

    Enriques–Kodaira_classification

  • Principal U(1)-bundle
  • Special type of principal bundle

    over the canonical inclusions U ⁡ ( 1 ) ⊂ C {\displaystyle \operatorname {U} (1)\subset \mathbb {C} } . Due to the single rank, the vector bundle is only

    Principal U(1)-bundle

    Principal U(1)-bundle

    Principal_U(1)-bundle

  • Musical isomorphism
  • Isomorphism between the tangent and cotangent bundles of a manifold

    isomorphism (or canonical isomorphism) is an isomorphism between the tangent bundle T M {\displaystyle \mathrm {T} M} and the cotangent bundle T ∗ M {\displaystyle

    Musical isomorphism

    Musical_isomorphism

  • Supermanifold
  • Supergeometric generalization of a manifold

    a spin structure, that is, a square root of its canonical bundle (equivalently, of its tangent bundle). (This is a definition of split super Riemann structures

    Supermanifold

    Supermanifold

  • Algebraic geometry of projective spaces
  • negativity of the canonical line bundle makes projective spaces prime examples of Fano varieties, equivalently, their anticanonical line bundle is ample (in

    Algebraic geometry of projective spaces

    Algebraic_geometry_of_projective_spaces

  • Principal SU(2)-bundle
  • Special type of principal bundle

    Principal SU ⁡ ( 2 ) {\displaystyle \operatorname {SU} (2)} -bundles are generalizations of canonical projections B × SU ⁡ ( 2 ) ↠ B {\displaystyle B\times \operatorname

    Principal SU(2)-bundle

    Principal_SU(2)-bundle

  • Kodaira surface
  • usually divided into two subtypes: primary Kodaira surfaces with trivial canonical bundle, and secondary Kodaira surfaces which are quotients of these by finite

    Kodaira surface

    Kodaira_surface

  • G-structure on a manifold
  • Structure group sub-bundle on a tangent frame bundle

    has a canonical G L ( n ) {\displaystyle GL(n)} -bundle, the frame bundle. In particular, every smooth manifold has a canonical vector bundle, the tangent

    G-structure on a manifold

    G-structure_on_a_manifold

  • Glossary of classical algebraic geometry
  • 1, p. 47) canonical 1.  The canonical series is the linear series of the canonical line bundle 2.  The canonical bundle is the line bundle of differential

    Glossary of classical algebraic geometry

    Glossary_of_classical_algebraic_geometry

  • Coherent sheaf cohomology
  • Concept in algebraic geometry

    {\displaystyle L} is an ample line bundle on X {\displaystyle X} , and K X {\displaystyle K_{X}} a canonical bundle, then H j ( X , K X ⊗ L ) = 0 {\displaystyle

    Coherent sheaf cohomology

    Coherent_sheaf_cohomology

  • Hilbert scheme
  • Moduli scheme of subschemes of a scheme, represents the flat-family-of-subschemes functor

    with c 1 = 0 {\displaystyle c_{1}=0} (K3 surface or a torus). The canonical bundle of M is trivial, as follows from the Kodaira classification of surfaces

    Hilbert scheme

    Hilbert_scheme

  • Huai-Dong Cao
  • Chinese mathematician

    of gradient steady Kähler-Ricci solitons on the total space of the canonical bundle over complex projective space which is complete and rotationally symmetric

    Huai-Dong Cao

    Huai-Dong_Cao

  • Frame bundle
  • Principal bundle associated to a vector bundle

    In mathematics, a frame bundle is a principal fiber bundle F ( E ) {\displaystyle F(E)} associated with any vector bundle E {\displaystyle E} . The fiber

    Frame bundle

    Frame bundle

    Frame_bundle

  • Vojta's conjecture
  • On heights of points on algebraic varieties over number fields

    {\displaystyle P\in U(F)} . Let X {\displaystyle X} be a variety with trivial canonical bundle, for example, an abelian variety, a K3 surface or a Calabi-Yau variety

    Vojta's conjecture

    Vojta's_conjecture

  • Holomorphic tangent bundle
  • into the complexified tangent bundle, and then projection onto the i {\displaystyle i} -eigenbundle. The canonical bundle is defined by K M = Λ n T 1

    Holomorphic tangent bundle

    Holomorphic_tangent_bundle

  • Complex vector bundle
  • vector bundle is canonically oriented; in particular, one can take its Euler class. A complex vector bundle is a holomorphic vector bundle if X {\displaystyle

    Complex vector bundle

    Complex_vector_bundle

  • Connection (principal bundle)
  • Concept in mathematics

    transport on the bundle; that is, a way to "connect" or identify fibers over nearby points. A principal G-connection on a principal G-bundle P {\displaystyle

    Connection (principal bundle)

    Connection_(principal_bundle)

  • Orientation of a vector bundle
  • Generalization of an orientation of a vector space

    oriented bundle gives rise to a Gysin sequence. A complex vector bundle is oriented in a canonical way. The notion of an orientation of a vector bundle generalizes

    Orientation of a vector bundle

    Orientation_of_a_vector_bundle

  • Clifford module bundle
  • algebras. The canonical example is a spinor bundle. In fact, on a Spin manifold, every Clifford module is obtained by twisting the spinor bundle. The notion

    Clifford module bundle

    Clifford_module_bundle

  • Fourier–Mukai transform
  • Fourier–Mukai transform gives examples of different varieties (with trivial canonical bundles) that have equivalent derived categories. Let g denote the dimension

    Fourier–Mukai transform

    Fourier–Mukai_transform

  • Normal bundle
  • Concept in mathematics

    a field of mathematics, a normal bundle is a particular kind of vector bundle, complementary to the tangent bundle, and coming from an embedding (or

    Normal bundle

    Normal_bundle

  • Canonical transformation
  • Coordinate transformation that preserves the form of Hamilton's equations

    In Hamiltonian mechanics, a canonical transformation is a change of canonical coordinates (q, p) → (Q, P) that preserves the form of Hamilton's equations

    Canonical transformation

    Canonical_transformation

  • Dual bundle
  • Mathematical operation on vector bundles

    the dual bundle is an operation on vector bundles extending the operation of duality for vector spaces. The dual bundle of a vector bundle π : E → X

    Dual bundle

    Dual_bundle

  • Fano surface
  • of the universal rank 2 bundle on G. We have the: Tangent bundle Theorem (Fano, Clemens-Griffiths, Tyurin): The tangent bundle of S is isomorphic to U

    Fano surface

    Fano_surface

  • Flip (algebraic geometry)
  • Surgery operation in minimal model program

    {\displaystyle f\colon X\to Y} is a morphism, and K is the canonical bundle of X, then the relative canonical ring of f is ⨁ m f ∗ ( O X ( m K ) ) {\displaystyle

    Flip (algebraic geometry)

    Flip_(algebraic_geometry)

  • Supersingular variety
  • Mathematical concept

    Frobenius action, trivial canonical bundle, and its Picard scheme Picτ is isomorphic to the group scheme α2. Its canonical double cover is a purely inseparable

    Supersingular variety

    Supersingular_variety

  • Moduli of algebraic curves
  • Geometric space

    {\displaystyle \omega _{C}} . But, using Riemann–Roch shows the degree of the canonical bundle is − 2 {\displaystyle -2} , so the degree of ω C ⊗ 2 {\displaystyle

    Moduli of algebraic curves

    Moduli of algebraic curves

    Moduli_of_algebraic_curves

  • Kawamata–Viehweg vanishing theorem
  • if L is a big nef line bundle (for example, an ample line bundle) on a complex projective manifold with canonical line bundle K, then the coherent cohomology

    Kawamata–Viehweg vanishing theorem

    Kawamata–Viehweg_vanishing_theorem

  • Indigenous bundle
  • Type of fiber bundle on a Riemann surface

    indigenous bundle on a Riemann surface is a fiber bundle with a flat connection associated to some complex projective structure. Indigenous bundles were introduced

    Indigenous bundle

    Indigenous_bundle

  • Tensor product bundle
  • line bundle, then E ⊗ O = E for any E. Example: E ⊗ E∗ is canonically isomorphic to the endomorphism bundle End(E), where E∗ is the dual bundle of E.

    Tensor product bundle

    Tensor_product_bundle

  • Shigefumi Mori
  • Japanese mathematician (born 1951)

    1007/s00229-002-0336-2. S2CID 121266346. Mori, Shigefumi (1982). "Threefolds Whose Canonical Bundles Are Not Numerically Effective". Annals of Mathematics. 116 (1): 133–176

    Shigefumi Mori

    Shigefumi Mori

    Shigefumi_Mori

  • Abel–Jacobi map
  • Construction in algebraic geometry

    {\displaystyle H^{0}(C,K)\cong \mathbb {C} ^{g},} where K is the canonical bundle on C. By definition, this is the space of globally defined holomorphic

    Abel–Jacobi map

    Abel–Jacobi_map

  • List of algebraic geometry topics
  • Elimination theory Gröbner basis Projective variety Quasiprojective variety Canonical bundle Complete intersection Serre duality Spaltenstein variety Arithmetic

    List of algebraic geometry topics

    List_of_algebraic_geometry_topics

  • Néron–Tate height
  • ^{n}} of degree d > 1 {\displaystyle d>1} yields a canonical height associated to the line bundle relation φ ∗ O ( 1 ) = O ( n ) {\displaystyle \varphi

    Néron–Tate height

    Néron–Tate_height

  • Chiral algebra
  • {M}}\boxtimes {\mathcal {N}}(n\Delta ),} Ω {\displaystyle \Omega } is the canonical bundle, and the 'diagonal extension by delta-functions' Δ ! {\displaystyle

    Chiral algebra

    Chiral_algebra

  • Jean-Pierre Demailly
  • French mathematician (1957–2022)

    uniruled if and only if its canonical bundle K X {\displaystyle K_{X}} is not pseudo-effective. For a singular metric on a line bundle, Nadel, Demailly, and

    Jean-Pierre Demailly

    Jean-Pierre Demailly

    Jean-Pierre_Demailly

  • Ruled variety
  • over a field of characteristic zero is uniruled if and only if the canonical bundle of X is not pseudo-effective (that is, not in the closed convex cone

    Ruled variety

    Ruled_variety

  • Solder form
  • Mathematical construct of fiber bundles

    one-form, the canonical one-form, or the symplectic potential. Consider the Mobius strip as a fiber bundle over the circle. The vertical bundle o*VE is still

    Solder form

    Solder form

    Solder_form

  • Affine bundle
  • Type of fiber bundle

    {y}}^{j}} . An affine bundle has a global section, but in contrast with vector bundles, there is no canonical global section of an affine bundle. Let π : Y → X

    Affine bundle

    Affine_bundle

  • Divisor (algebraic geometry)
  • Generalizations of codimension-1 subvarieties of algebraic varieties

    isomorphism to define the canonical divisor KX of X: it is the Weil divisor (up to linear equivalence) corresponding to the line bundle of differential forms

    Divisor (algebraic geometry)

    Divisor_(algebraic_geometry)

  • Jet bundle
  • Construction in differential topology

    differential topology, the jet bundle is a certain construction that makes a new smooth fiber bundle out of a given smooth fiber bundle. It makes it possible to

    Jet bundle

    Jet_bundle

  • Prym differential
  • Equivalently it is a section of a certain line bundle on the Riemann surface in the same component as the canonical bundle. Prym differentials were introduced by

    Prym differential

    Prym_differential

  • Connection (vector bundle)
  • Defines a notion of parallel transport on a bundle

    (the trivial line bundle over M). More generally, there is a canonical flat connection on any flat vector bundle (i.e. a vector bundle whose transition

    Connection (vector bundle)

    Connection_(vector_bundle)

  • Logarithmic form
  • Meromorphic differential form

    Because the canonical bundle K P 2 = Ω P 2 2 {\displaystyle K_{\mathbf {P} ^{2}}=\Omega _{\mathbf {P} ^{2}}^{2}} is isomorphic to the line bundle O ( − 3

    Logarithmic form

    Logarithmic_form

  • Canonical connection
  • Topics referred to by the same term

    differential geometry), a canonical connection can mean either A canonical connection on a symmetric space that is canonically defined (as described in

    Canonical connection

    Canonical_connection

  • Connection (affine bundle)
  • connection on a vector bundle Y → X is a sum of a linear connection and a basic soldering form on Y → X. Due to the canonical vertical splitting VY =

    Connection (affine bundle)

    Connection_(affine_bundle)

  • Geometric genus
  • Property of algebraic varieties and complex manifolds

    Kähler differentials and the power is the (top) exterior power, the canonical line bundle. The geometric genus is the first invariant pg = P1 of a sequence

    Geometric genus

    Geometric_genus

  • Local twistor
  • Vector bundle associated with conformal manifolds

    conformal Cartan connection. That is, there is a canonical marked one-dimensional subspace X in the tractor bundle, and Π {\displaystyle \Pi } is the annihilator

    Local twistor

    Local_twistor

  • Hamiltonian mechanics
  • Formulation of classical mechanics using momenta

    {\displaystyle ({\boldsymbol {q}},{\boldsymbol {\dot {q}}})} on the tangent bundle T M . {\displaystyle TM.} The quantities p i ( q , q ˙ , t )   = def   ∂

    Hamiltonian mechanics

    Hamiltonian mechanics

    Hamiltonian_mechanics

  • Infinite-dimensional sphere
  • Limit of spheres in algebraic topology

    {\displaystyle \operatorname {O} (1)} -bundle S n ↠ R P n {\displaystyle S^{n}\twoheadrightarrow \mathbb {R} P^{n}} is then the canonical inclusion i : R P n ↪ R P

    Infinite-dimensional sphere

    Infinite-dimensional_sphere

  • Affine gauge theory
  • Gauge theory with affine connections

    _{\mu }} due to the canonical isomorphism V A T X = A T X × X T X {\displaystyle VATX=ATX\times _{X}TX} of the vertical tangent bundle V A T X {\displaystyle

    Affine gauge theory

    Affine_gauge_theory

  • Symplectic manifold
  • Type of manifold in differential geometry

    called the Poincaré two-form or the canonical two-form. Thus, we can locally think of M as being the cotangent bundle T ∗ R n {\displaystyle T^{*}\mathbb

    Symplectic manifold

    Symplectic_manifold

AI & ChatGPT searchs for online references containing CANONICAL BUNDLE

CANONICAL BUNDLE

AI search references containing CANONICAL BUNDLE

CANONICAL BUNDLE

  • Prime
  • Surname or Lastname

    English

    Prime

    English : from a Middle English personal name or nickname. The personal name existed in Old English, and is probably derived from Old English prim ‘early morning’ (from Latin primus ‘first’, used as the name of one of the canonical hours). The surname may be derived from this word as a Middle English nickname in the sense ‘fine’, ‘excellent’.French : feminine form of Prim 3.Dutch : variant of Priem.Probably an Americanized spelling of German Preim, a topographic name (of Slavic origin), perhaps from a river near Hannover; or of Preime, a variant of Primus.

    Prime

  • Omer
  • Boy/Male

    American, Arabic, Australian, French, Hebrew, Latin

    Omer

    Eloquent or Bundle of Grain; First Son; Long Living

    Omer

  • Packard
  • Surname or Lastname

    English

    Packard

    English : from Middle English pa(c)k ‘pack’, ‘bundle’ + the Anglo-Norman French pejorative suffix -ard, hence a derogatory occupational name for a peddler.English : pejorative derivative of the Middle English personal name Pack.English : from a Norman personal name, Pachard, Baghard, composed of the Germanic elements pac, bag ‘fight’ + hard ‘hardy’, ‘brave’, ‘strong’.Probably an Americanized spelling of German Packert, Päckert, from Germanic personal names formed with a word meaning ‘battle’ or ‘to fight’; or a variant of Packer 2 (with excrescent -t).

    Packard

  • Truss
  • Surname or Lastname

    English

    Truss

    English : occupational nickname for a peddler, from Old French trousse ‘bundle’, ‘pack’.Ukrainian : nickname from trus ‘rabbit’, typically applied to someone thought to be a coward.

    Truss

  • Durapa
  • Boy/Male

    Indian

    Durapa

    Bundle of Joy

    Durapa

  • Sheaff
  • Surname or Lastname

    English (Kent)

    Sheaff

    English (Kent) : from Middle English shefe ‘sheaf’, ‘bundle’ (Old English scēaf), hence possibly a metonymic occupational name for a harvest worker, or for someone who paid or collected tithes, from the same term in the sense ‘tenth’ (or other proportion of produce paid as a tithe).Jacob Sheafe (d. 1658) was one of the founds of Boston MA. He is buried in the King’s Chapel Burying Ground there.

    Sheaff

  • Cannon
  • Surname or Lastname

    Irish

    Cannon

    Irish : Anglicized form of Gaelic Mac Canann or Ó Canann (Ulster), or Ó Canáin (County Galway) ‘son (Mac) or descendant (Ó) of Canán’, a personal name derived from cano ‘wolf cub’. In Ulster it may also be from Ó Canannáin ‘descendant of Canannán’, a diminutive of the personal name.English : from Middle English canun ‘canon’ (Old Norman French canonie, canoine, from Late Latin canonicus). In medieval England this term denoted a clergyman living with others in a clergy house; the surname is mostly an occupational name for a servant in a house of canons, although it could also be a nickname or even a patronymic.

    Cannon

  • Balon
  • Surname or Lastname

    English

    Balon

    English : from Old French balon ‘bundle’, ‘roll’, ‘pack’, hence a nickname for a small, rotund man or possibly a metonymic occupational name for a carrier of goods and merchandise.French (Bâlon) : generally regarded as a habitational name from Baalons in the Ardennes, it may however simply be from balon ‘ball’, ‘roll’ (see 1) or a derivative of Bal.

    Balon

  • Dicker
  • Surname or Lastname

    English (southwest)

    Dicker

    English (southwest) : occupational name for a digger of ditches or a builder of dikes, or a topographic name for someone who lived by a ditch or dike, from an agent derivative of Middle English diche, dike (see Dyke).English : regional name from an area of East Sussex, near Hellingly, called ‘the Dicker’ (hence also the hamlets of Upper and Lower Dicker), from Middle English dyker unit of ten (Latin decuria, from decem ‘ten’); the reason for the place being so named is not clear. It has been suggested that the reference is to a bundle of iron rods, in which sense dicras appears in Domesday Book. Such a bundle could have been the rent for property in this iron-working area. Surname forms such as atte dicker occur in the surrounding region in the 13th and 14th centuries.German and Jewish (Ashkenazic) : variant of Dick 2, from an inflected form.North German : variant of Low German Dieker, a topographic or an occupational name for someone who lived or worked at a dike (see Dieck).Americanized spelling of French Decaire.

    Dicker

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Online names & meanings

  • Bitasok | பிதாஸோக
  • Boy/Male

    Tamil

    Bitasok | பிதாஸோக

    One who does not mourn

  • OROCHI
  • Male

    Japanese

    OROCHI

    (大蛇) Japanese name OROCHI means "big snake." In mythology, this is the name of an eight-forked serpent who demanded virgin sacrifices. He was killed by the god-hero Susanoo.

  • Filicia
  • Girl/Female

    French

    Filicia

    Great happiness.

  • Ahovira
  • Boy/Male

    Indian, Sanskrit

    Ahovira

    Very Strong; A Sage

  • Waheebah |
  • Girl/Female

    Muslim

    Waheebah |

    One who gives, Giver, Donor

  • AbdulGhafoor
  • Boy/Male

    Arabic, Muslim

    AbdulGhafoor

    Servant of the Forgiver

  • Jerick
  • Boy/Male

    English

    Jerick

    Strong; gifted ruler. Blend of Jer- and Derrick.

  • Batal |
  • Boy/Male

    Muslim

    Batal |

    Brave, Champion, Hero

  • Arinderjit
  • Boy/Male

    Indian

    Arinderjit

    Gentalman

  • Mahafuzur | مہافوضور
  • Boy/Male

    Muslim

    Mahafuzur | مہافوضور

    Heart of Love in the sea

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Other words and meanings similar to

CANONICAL BUNDLE

AI search in online dictionary sources & meanings containing CANONICAL BUNDLE

CANONICAL BUNDLE

  • Anthropophagite
  • n.

    A cannibal.

  • Uncanonize
  • v. t.

    To deprive of canonical authority.

  • Canonicate
  • n.

    The office of a canon; a canonry.

  • Conical
  • a.

    Having the form of, or resembling, a geometrical cone; round and tapering to a point, or gradually lessening in circumference; as, a conic or conical figure; a conical vessel.

  • Plano-conical
  • a.

    Plane or flat on one side, and conical on the other.

  • Laconical
  • a.

    Expressing much in few words, after the manner of the Laconians or Spartans; brief and pithy; brusque; epigrammatic. In this sense laconic is the usual form.

  • Subconical
  • a.

    Slightly conical.

  • Chronical
  • a.

    Chronic.

  • Canonically
  • adv.

    In a canonical manner; according to the canons.

  • Laconical
  • a.

    See Laconic, a.

  • Laconic
  • a.

    Alt. of Laconical

  • Ecclesiastes
  • a.

    One of the canonical books of the Old Testament.

  • Canonicals
  • n. pl.

    The dress prescribed by canon to be worn by a clergyman when officiating. Sometimes, any distinctive professional dress.

  • Aaronic
  • a.

    Alt. of Aaronical

  • Aaronical
  • a.

    Pertaining to Aaron, the first high priest of the Jews.

  • Colonical
  • a.

    Of or pertaining to husbandmen.

  • Canonic
  • a.

    Alt. of Cannonical

  • Canonicalness
  • n.

    The quality of being canonical; canonicity.

  • Cannonical
  • a.

    Of or pertaining to a canon; established by, or according to a , canon or canons.

  • Laconical
  • a.

    Laconian; characteristic of, or like, the Spartans; hence, stern or severe; cruel; unflinching.