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Study of complex manifolds and several complex variables
complex geometry is the study of geometric structures and constructions arising out of, or described by, the complex numbers. In particular, complex geometry
Complex_geometry
Branch of mathematics
relations between complex geometry and algebraic geometry. The primary objects of study in complex geometry are complex manifolds, complex algebraic varieties
Geometry
Central atom with four substituents located at the corners of a tetrahedron
than a bonded atom.[citation needed] Again the geometry is widespread, particularly so for complexes where the metal has d0 or d10 configuration. Illustrative
Tetrahedral molecular geometry
Tetrahedral_molecular_geometry
Overview of and topical guide to geometry
Absolute geometry Affine geometry Algebraic geometry Analytic geometry Birational geometry Complex geometry Computational geometry Conformal geometry Constructive
Outline_of_geometry
Two closely related mathematical subjects
algebraic geometry and analytic geometry are two closely related subjects. While algebraic geometry studies algebraic varieties, analytic geometry deals with
Algebraic geometry and analytic geometry
Algebraic_geometry_and_analytic_geometry
Branch of mathematics
Algebraic geometry occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex analysis
Algebraic_geometry
Branch of differential geometry and differential topology
interchangeably with "symplectic geometry". The name "complex group" formerly advocated by me in allusion to line complexes, as these are defined by the vanishing
Symplectic_geometry
Branch of mathematics
Differential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds.
Differential_geometry
Manifold
In differential geometry and complex geometry, a complex manifold or a complex analytic manifold is a manifold with a complex structure, that is an atlas
Complex_manifold
Maths textbook
Geometry of Complex Numbers is an undergraduate textbook on geometry, whose topics include circles, the complex plane, inversive geometry, and non-Euclidean
Geometry_of_Complex_Numbers
Creating a complex 3D surface or object by combining primitive objects
Constructive solid geometry (CSG; formerly called computational binary solid geometry) is a technique used in solid modeling. Constructive solid geometry allows a
Constructive_solid_geometry
Mathematical concept in algebraic geometry
rational functions on V. In classical algebraic geometry they are ratios of polynomials; in complex geometry these are meromorphic functions and their higher-dimensional
Function field of an algebraic variety
Function_field_of_an_algebraic_variety
Branch of mathematics studying functions of a complex variable
functions of one or more complex variables. It is used in many branches of mathematics, including functional analysis, algebraic geometry, number theory, analytic
Complex_analysis
Area of mathematics using condensed sets
unify various mathematical subfields, including topology, complex geometry, and algebraic geometry.[citation needed] In particular, Kiran Kedlaya described
Condensed_mathematics
Generalization of a complex manifold that allows the use of singularities
particularly differential geometry and complex geometry, a complex analytic variety or complex analytic space is a generalization of a complex manifold that allows
Complex_analytic_variety
Molecular geometry
In chemistry, octahedral molecular geometry, also called square bipyramidal, describes the shape of compounds with six atoms or groups of atoms or ligands
Octahedral_molecular_geometry
Artificial intelligence (AI) program
AlphaGeometry is an artificial intelligence (AI) program that can solve hard problems in Euclidean geometry. The system comprises a data-driven large language
AlphaGeometry
Property of a differential manifold that includes complex structures
differential geometry, a generalized complex structure is a property of a differential manifold that includes as special cases a complex structure and
Generalized_complex_structure
Two geometries based on axioms closely related to those specifying Euclidean geometry
non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the
Non-Euclidean_geometry
In organometallic chemistry, a "constrained geometry complex" (CGC) is a kind of catalyst used for the production of polyolefins such as polyethylene and
Constrained_geometry_complex
Unsolved problem in geometry
unsolved problem in algebraic geometry and complex geometry that relates the algebraic topology of a non-singular complex algebraic variety to its subvarieties
Hodge_conjecture
Number with a real and an imaginary part
"Number/Complex Numbers". Analytic continuation Circular motion using complex numbers Complex-base system Complex coordinate space Complex geometry Geometry of
Complex_number
Type of geometry
projective geometry are simpler statements. For example, the different conic sections are all equivalent in (complex) projective geometry, and some theorems
Projective_geometry
Geometric representation of the complex numbers
and hence “complex planes”. These are the quadratic algebras over the real number field. Complex coordinate space Complex geometry Complex line Constellation
Complex_plane
Molecular geometry of five coplanar atoms
transition metal complexes. The noble gas compound xenon tetrafluoride adopts this structure as predicted by VSEPR theory. The geometry is prevalent for
Square planar molecular geometry
Square_planar_molecular_geometry
Mathematical condition
physics, particularly in the context of electromagnetism and differential geometry, where it relates to the fact that the boundary of a boundary is always
Poincaré_lemma
combustion instability. Although it is much harder to predict, complex grain geometries offer another technique for increasing regression rate and burn
Hybrid_rocket_fuel_regression
Indian mathematician and monk of the Ramakrishna Order (born 1968)
best known for his work in hyperbolic geometry, geometric group theory, low-dimensional topology and complex geometry. Mahan Mitra studied at St. Xavier's
Mahan_Mj
In algebraic geometry, a complex algebraic variety is an algebraic variety (in the scheme sense or otherwise) over the field of complex numbers. Chow's
Complex_algebraic_variety
Manifold with inversion symmetry
spaces appear in the theory of Jordan triple systems, several complex variables, complex geometry, automorphic forms and group representations, in particular
Hermitian_symmetric_space
Mathematical concept
discussion). Complex projective space was first introduced by von Staudt (1860) as an instance of what was then known as the "geometry of position",
Complex_projective_space
Generalization of a polytope in real space
In geometry, a complex polytope is a generalization of a polytope in real space to an analogous structure in a complex Hilbert space, where each real
Complex_polytope
Statement in complex analysis
lemma, named after Hermann Amandus Schwarz, is a result in complex differential geometry that estimates the (squared) pointwise norm | ∂ f | 2 {\displaystyle
Schwarz_lemma
Fundamental operation on complex numbers
descriptions of redirect targets Complex conjugate line – Operation in complex geometry Complex conjugate representation Complex conjugate vector space – Mathematics
Complex_conjugate
Manifold with Riemannian, complex and symplectic structure
and especially differential geometry, a Kähler manifold is a manifold with three mutually compatible structures: a complex structure, a Riemannian structure
Kähler_manifold
On the Euler characteristic of a holomorphic vector bundle on a compact complex manifold
Hirzebruch,Topological Methods in Algebraic Geometry ISBN 3-540-58663-6 Huybrechts, Daniel (2004-11-18). Complex geometry: An introduction. Universitext. Springer
Hirzebruch–Riemann–Roch theorem
Hirzebruch–Riemann–Roch_theorem
Mathematics concept
complex geometry where they play an essential role in the definition of almost complex manifolds, by contrast to complex manifolds. The term "complex
Linear_complex_structure
Belgian mathematician
He introduced the concept of weights and tested them on objects in complex geometry. He also collaborated with David Mumford on a new description of the
Pierre_Deligne
Skeletonized version of algebraic geometry
In mathematics, tropical geometry is the study of polynomials and their geometric properties when addition is replaced with minimization and multiplication
Tropical_geometry
is thus generally synonymous with the complex line, not the complex coordinate plane. Algebraic geometry Complex vector Riemann sphere Brass, Peter; Moser
Complex_line
Operation in complex geometry
In complex geometry, the complex conjugate line of a straight line is the line that it becomes by taking the complex conjugate of each point on this line
Complex_conjugate_line
Italian mathematician
Fino is an Italian mathematician specializing in differential geometry, complex geometry, and Lie groups. She is a professor of mathematics in the Giuseppe
Anna_Fino
Canadian-American mathematician (1925–2020)
partial differential equations and the Newlander–Nirenberg theorem in complex geometry. He is regarded as a foundational figure in the field of geometric
Louis_Nirenberg
of complex analysis are applied to generating functions. Analytic geometry 1. Also known as Cartesian geometry, the study of Euclidean geometry using
Glossary of areas of mathematics
Glossary_of_areas_of_mathematics
Generalized residue for several complex variables
residue is a generalization, to several complex variables and complex manifold theory, of the residue at a pole of complex function theory. It is just one of
Poincaré_residue
Vanishing theorem for multiplier ideals
(2000). "On the Ohsawa-Takegoshi-Manivel L 2 extension theorem". Complex Analysis and Geometry. Progress in Mathematics. Vol. 188. pp. 47–82. doi:10.1007/978-3-0348-8436-5_3
Nadel_vanishing_theorem
American mathematician
the University of Toronto, where he wrote "Representation Theory and Complex Geometry" with Ginzburg. At Toronto, John M. Liew introduced Chriss to "quant"
Neil_Chriss
Branch of geometry that studies combinatorial properties and constructive methods
Discrete geometry and combinatorial geometry are branches of geometry that study combinatorial properties and constructive methods of discrete geometric
Discrete_geometry
Study of angle-preserving transformations
In geometry, inversive geometry is the study of inversion, a transformation of the Euclidean plane that maps circles or lines to other circles or lines
Inversive_geometry
South Korean mathematician (born 1963)
South Korean mathematician, specializing in algebraic geometry and complex differential geometry. Hwang is the eldest son of gayageum musician Hwang Byungki
Jun-Muk_Hwang
In complex geometry, the term positive form refers to several classes of real differential forms of Hodge type (p, p). Real (p,p)-forms on a complex manifold
Positive_form
Vietnamese-American mathematician
He is known for his research on complex analysis, partial differential equations, string theory and complex geometry. After graduating from Lycée Jean-Jacques
Duong_Hong_Phong
Curve from a cone intersecting a plane
Projective Geometry: A Guided Tour Through Real and Complex Geometry. Springer. ISBN 9783642172854. Samuel, Pierre (1988), Projective Geometry, Undergraduate
Conic_section
Complex-differentiable (mathematical) function
a complex-valued function of one or more complex variables that is complex differentiable in a neighbourhood of each point in a domain in complex coordinate
Holomorphic_function
Model of the extended complex plane plus a point at infinity
geometry, the Riemann sphere is the prototypical example of a Riemann surface, and is one of the simplest complex manifolds. In projective geometry,
Riemann_sphere
(algebraic geometry) Chow's theorem (algebraic geometry) Cramer's theorem (algebraic curves) (analytic geometry) Hartogs's theorem (complex analysis) Hartogs's
List_of_theorems
Branch of mathematics
of eight possible geometries. 2-dimensional topology can be studied as complex geometry in one variable (Riemann surfaces are complex curves) – by the
Topology
Italian mathematician (born c.1981)
Mathematical Sciences. Tosatti does research on complex and differential geometry; geometric analysis on complex, Hermitian, and symplectic manifolds; and partial
Valentino_Tosatti
Spiral scroll-like ornament that forms the basis of the Ionic order
furniture design, silverware and ceramics. A method of drawing the complex geometry was devised by the ancient Roman architect Vitruvius through the study
Volute
It is a generalization of the Lie bracket from an operation on the tangent bundle
Today a complex version of the p = 1 {\displaystyle p=1} Courant bracket plays a central role in the field of generalized complex geometry, introduced
Courant_bracket
Chilean mathematician
Iberoamerican Congress on Geometry, and former president of the Chilean Mathematical Society. Her research specialties include complex geometry, Fuchsian groups
Rubí_Rodríguez
Theoretical object in mathematics
symmetries in projective geometry and the combinatorics of simplicial complexes. F1 has been connected to noncommutative geometry and to a possible proof
Field_with_one_element
Class of mathematical function
In complex analysis, a meromorphic function on an open subset D {\displaystyle D} of the complex plane is a function that is holomorphic on all of D {\displaystyle
Meromorphic_function
Romanian mathematician
22 June 1965, Brașov) is a Romanian mathematician, specializing in complex geometry, global analysis, and spectral theory. Marinescu received from the
George Marinescu (mathematician)
George_Marinescu_(mathematician)
Cohomology theory for complex manifolds
In complex geometry in mathematics, Bott–Chern cohomology is a cohomology theory for complex manifolds. It serves as a bridge between de Rham cohomology
Bott–Chern_cohomology
symplectic geometry. He was an invited speaker at the International Congress of Mathematicians in 2014, speaking in the section on "Algebraic and Complex Geometry"
Bertrand_Toën
In mathematics, and especially complex geometry, the holomorphic tangent bundle of a complex manifold M {\displaystyle M} is the holomorphic analogue
Holomorphic_tangent_bundle
Technical drawing of a building or building project
and opening up new possibilities of form using organic shapes and complex geometry. Today, most architectural drawings are created using CAD software
Architectural_drawing
Complex convexity is a general term in complex geometry. A set Ω {\displaystyle \Omega } in C n {\displaystyle \mathbb {C} ^{n}} is called C {\displaystyle
Complex_convexity
implement custom models OpenLB supports complex data structures that allow simulations in complex geometries and parallel execution using MPI, OpenMP
OpenLB
Mathematical model of the physical space
Euclidean geometry is a mathematical system attributed to Euclid, an ancient Greek mathematician, which he described in his textbook on geometry, Elements
Euclidean_geometry
Attribute of a mathematical function
In mathematics, more specifically complex analysis, the residue of a function at a point of its domain is a complex number proportional to the contour
Residue_(complex_analysis)
Theorem in complex analysis
In complex analysis, Liouville's theorem states that every bounded entire function must be constant. That is, every holomorphic function f {\displaystyle
Liouville's theorem (complex analysis)
Liouville's_theorem_(complex_analysis)
Mathematician
needed]) was a mathematician working in differential geometry, general relativity, and complex geometry. He was a research professor at the Chinese University
Luen-Fai_Tam
Straight figure with zero width and depth
In geometry, a straight line, usually abbreviated line, is an infinitely long object with no width, depth, or curvature. It is a special case of a curve
Line_(geometry)
Topics referred to by the same term
former name of the club's stadium Skoda–El Mir theorem, theorem of complex geometry This disambiguation page lists articles associated with the title Skoda
Skoda
Mathematical manifold theory
the study of complex projective varieties, is encompassed by the latter case. Hodge theory has become an important tool in algebraic geometry, particularly
Hodge_theory
Gives general conditions under which sheaf cohomology groups with indices > 0 are zero
Kodaira vanishing theorem is a basic result of complex manifold theory and complex algebraic geometry, describing general conditions under which sheaf
Kodaira_vanishing_theorem
American physicist
multiplets and their implications for nonlinear sigma models, generalized complex geometry, and duality in supersymmetric theories. He has also authored more
Sylvester_James_Gates
Generalizes the Kodaira vanishing theorem for ample vector bundle
In algebraic geometry, Le Potier's vanishing theorem is an extension of the Kodaira vanishing theorem, on vector bundles. The theorem states the following
Le_Potier's_vanishing_theorem
1998 video game
triangular polygons, allowing developers to achieve greater detail and more complex geometry. The game was designed to be more in line with the puzzle-solving gameplay
Tomb_Raider_III
Classifies holomorphic vector bundles over the complex projective line
1112/S0010437X15007484. S2CID 119716554. Huybrechts, Daniel (2004-11-18). Complex geometry: An introduction. Universitext. Springer Science+Business Media. ISBN 978-3540212904
Birkhoff–Grothendieck_theorem
The mapping is quite tedious if it involves Complex geometry. In order to model this type of geometry we divide the flow region into various smaller
Grid_classification
theories of algebraic geometry and complex manifolds. It is named after Takao Fujita, who formulated it in 1985. In complex geometry, the conjecture states
Fujita_conjecture
Generalizes the Kodaira vanishing theorem
4417 [math.CV]. Kobayashi, Shoshichi (2014-07-14). Differential Geometry of Complex Vector Bundles. Princeton University Press. p. 68. ISBN 9781400858682
Nakano_vanishing_theorem
Mathematical model for turbulence
its cost prohibits simulation of practical engineering systems with complex geometry or flow configurations, such as turbulent jets, pumps, vehicles, and
Large_eddy_simulation
Parametrizes complex structures on a surface
Gardiner, Frederic P.; Masur, Howard (1991), "Extremal length geometry of Teichmüller space", Complex Variables Theory Appl., 16 (2–3): 209–237, doi:10.1080/17476939108814480
Teichmüller_space
Topics referred to by the same term
bitmap with a transparent background used in 3D graphics to simulate complex geometry All pages with titles beginning with cutout All pages with titles beginning
Cut-out
Arrangement of steering linkages
Ackermann geometry gives each front wheel hub its own pivoted carrier (on solid axles this pivot is called a kingpin but on more complex suspension it
Ackermann_steering_geometry
Describes the line bundles on a complex torus or complex abelian variety
mathematics, the Appell–Humbert theorem describes the line bundles on a complex torus or complex abelian variety. It was proved for 2-dimensional tori by Appell (1891)
Appell–Humbert_theorem
On zeros of derivatives of cubic polynomials
geometric relationship between the zeroes of a third-degree polynomial with complex coefficients and the zeroes of its derivative. See also geometrical properties
Marden's_theorem
Riemannian manifold with SU(n) holonomy
In algebraic and differential geometry, a Calabi–Yau manifold, also known as a Calabi–Yau space, is a particular type of manifold which has certain properties
Calabi–Yau_manifold
Mathematical conjecture
In mathematics, specifically in the fields of model theory and complex geometry, Existential Closedness problems aim to determine when systems of equations
Existential closedness conjecture
Existential_closedness_conjecture
Mathematics of varieties with integer coordinates
geometry. The extensive development of algebraic geometry in the 20th century produced powerful tools to study these equations. Diophantine geometry is
Diophantine_geometry
in the field of complex geometry, a holomorphic curve in a complex manifold M is a non-constant holomorphic map f from the complex plane to M. Nevanlinna
Holomorphic_curve
Castle at Shanghai Disneyland
California, and Shanghai using cloud-based tools to coordinate the castle's complex geometry, structural systems, and themed detailing. Howard Brown, Senior Vice
Enchanted_Storybook_Castle
Chinese mathematician
1965) is a Chinese mathematician, specializing in several complex variables and complex geometry. He is known for his 1998 proof of the "extended future
Xiangyu_Zhou
French mathematician (1957–2022)
September 1957 – 17 March 2022) was a French mathematician who worked in complex geometry. He was a professor at Université Grenoble Alpes and a permanent member
Jean-Pierre_Demailly
Line along which a quadratic form applied to any two points' displacement is zero
isotropic quadratic form, and never with a definite quadratic form. Using complex geometry, Edmond Laguerre first suggested the existence of two isotropic lines
Isotropic_line
Study of space and shapes locally given by a convergent power series
locally. In the most common case the function has a domain and range in the complex plane. More formally, a map, f : U → V {\displaystyle f:U\rightarrow V\qquad
Geometric_function_theory
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