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CLASSICAL CURVES

  • Classical Curves
  • 2012 studio album by Jam City

    Classical Curves is the debut studio album by British producer Jam City. It was released on 28 May 2012 by Night Slugs. It received critical praise, and

    Classical Curves

    Classical_Curves

  • Jam City
  • UK electronic music producer and DJ

    label Night Slugs. He has released four full-length albums: 2012's Classical Curves, 2015's Dream a Garden, 2020's Pillowland, and 2023's EFM. He has also

    Jam City

    Jam_City

  • Classical modular curve
  • Plane algebraic curve

    modular curves. In particular it has another expression as a compactified quotient of the complex upper half-plane H. The classical modular curve, which

    Classical modular curve

    Classical_modular_curve

  • Dream a Garden
  • 2016 studio album by Jam City

    "not a total break from the world of Classical Curves, but rather an inversion," explaining that "Classical Curves is the surface, Dream a Garden is the

    Dream a Garden

    Dream_a_Garden

  • Moduli of algebraic curves
  • Geometric space

    algebraic geometry, a moduli space of curves is a space whose points correspond to isomorphism classes of algebraic curves. The term "modulus" was introduced

    Moduli of algebraic curves

    Moduli of algebraic curves

    Moduli_of_algebraic_curves

  • Near visual acuity
  • Clarity of near objects or letters

    accommodation amplitude on age is graphically summarized by Duane's classical curves. The difficulty in reading small prints or blurring at a reading distance

    Near visual acuity

    Near visual acuity

    Near_visual_acuity

  • List of curves
  • psychology, ecology, etc. Rational curves are subdivided according to the degree of the polynomial. Line Plane curves of degree 2 are known as conics or

    List of curves

    List_of_curves

  • Curve
  • Mathematical idealization of the trace left by a moving point

    the curve is called a parametrization, and the curve is a parametric curve. In this article, these curves are sometimes called topological curves to distinguish

    Curve

    Curve

    Curve

  • Galaxy rotation curve
  • Observed discrepancy in galactic angular momenta

    asymmetric, so that data from each side are averaged to create the curve. The experimental curves observed are at significant variance with gravitational theory

    Galaxy rotation curve

    Galaxy rotation curve

    Galaxy_rotation_curve

  • Algebraic curve
  • Curve defined as zeros of polynomials

    curves) Crunode Curve Curve sketching Jacobian variety Klein quartic List of curves Hilbert's sixteenth problem Cubic plane curve Hyperelliptic curve

    Algebraic curve

    Algebraic curve

    Algebraic_curve

  • Elliptic-curve cryptography
  • Approach to public-key cryptography

    elliptic-curve domain parameters to Special Publication 800-186. SP 800-186 includes previously recommended Weierstrass curves and two Edwards curves for EdDSA;

    Elliptic-curve cryptography

    Elliptic-curve cryptography

    Elliptic-curve_cryptography

  • Deconstructed club
  • Experimental electronic music genre

    of club music and tapping into the avant-garde. The Jam City album Classical Curves (2012) was an inspiration on the deconstructed club scene. UK musician

    Deconstructed club

    Deconstructed_club

  • Gallery of curves
  • a gallery of curves used in mathematics, by Wikipedia page. See also list of curves. Line Circle Ellipse Parabola Hyperbola Cubic curve Cubic polynomial

    Gallery of curves

    Gallery_of_curves

  • Weierstrass point
  • Point on a nonsingular algebraic curve

    are classical. Hermitian curves are an example of non-classical curves. These are projective curves defined over finite field G F ( q 2 ) {\displaystyle

    Weierstrass point

    Weierstrass_point

  • Curved Air
  • English progressive rock group

    Curved Air are an English progressive rock group formed in 1970 by musicians from mixed artistic backgrounds, including classical, folk and electronic

    Curved Air

    Curved Air

    Curved_Air

  • Accommodation (vertebrate eye)
  • Focusing ability of eye

    accommodation amplitude on age is graphically summarized by Duane's classical curves. The amplitude of accommodation is a clinical measurement that describes

    Accommodation (vertebrate eye)

    Accommodation (vertebrate eye)

    Accommodation_(vertebrate_eye)

  • Dragon curve
  • Fractal constructible with L-systems

    folding a strip of paper in half, although there are other curves that are called dragon curves that are generated differently. The Heighway dragon (also

    Dragon curve

    Dragon curve

    Dragon_curve

  • Yellow Sun (nuclear weapon)
  • First British operational high-yield strategic nuclear weapon warhead

    that it did not generate the complex pattern of shock waves that a classically curved nose created, which made it difficult to measure altitude barometrically

    Yellow Sun (nuclear weapon)

    Yellow Sun (nuclear weapon)

    Yellow_Sun_(nuclear_weapon)

  • Elliptic curve
  • Algebraic curve in mathematics

    enough to include all non-singular cubic curves; see § Elliptic curves over a general field below.) An elliptic curve is an abelian variety – that is, it has

    Elliptic curve

    Elliptic curve

    Elliptic_curve

  • Main Attrakionz
  • American hip-hop duo

    "Oooh" and "Ticky Tacky" from 51 (2012) Jam City – "The Nite Life" from Classical Curves (2012) Fat Tony and Tom Cruz – "Double Up" from Double Dragon (2012)

    Main Attrakionz

    Main_Attrakionz

  • Modular curve
  • Algebraic variety

    algebraic definition of modular curves, without reference to complex numbers, and, moreover, prove that modular curves are defined either over the field

    Modular curve

    Modular_curve

  • Pseudoholomorphic curve
  • marked points. The domain curve C {\displaystyle C} is an element of the Deligne–Mumford moduli space of curves. The classical case occurs when X {\displaystyle

    Pseudoholomorphic curve

    Pseudoholomorphic_curve

  • Bell's theorem
  • Theorem in physics

    {\displaystyle {\vec {c}}.} Experimental results contradict the classical curves and match the curve predicted by quantum mechanics as long as experimental shortcomings

    Bell's theorem

    Bell's_theorem

  • Cepheid variable
  • Type of variable star that pulsates radially

    the distinctive light curve shapes with the rapid increase in brightness and a hump, but some with more symmetrical light curves were known as Geminids

    Cepheid variable

    Cepheid variable

    Cepheid_variable

  • Novikov self-consistency principle
  • Principle suggesting that time travel paradoxes are inherently impossible

    relativity contain closed timelike curves—for example the Gödel metric. Novikov discussed the possibility of closed timelike curves (CTCs) in books he wrote in

    Novikov self-consistency principle

    Novikov_self-consistency_principle

  • Yield curve
  • Relationships among bond yields of different maturities

    Treasury curve for government bonds. Different markets publish related curves for different purposes. Common examples include government bond curves, overnight

    Yield curve

    Yield curve

    Yield_curve

  • Mordell curve
  • Elliptic curve

    These curves were closely studied by Louis Mordell, from the point of view of determining their integer points. He showed that every Mordell curve contains

    Mordell curve

    Mordell curve

    Mordell_curve

  • Elliptic-curve Diffie–Hellman
  • Key agreement protocol

    these two, other proposals of Montgomery curves can be found at. Curve25519 is a popular set of elliptic curve parameters and reference implementation

    Elliptic-curve Diffie–Hellman

    Elliptic-curve_Diffie–Hellman

  • Phillips curve
  • Economic model relating wages to unemployment

    formal analysis posits up to five groups/curves over the period. However, modified forms of the Phillips curve that take inflationary expectations into

    Phillips curve

    Phillips_curve

  • Classical conditioning
  • Aspect of learning procedure

    Classical conditioning (also respondent conditioning and Pavlovian conditioning) is a behavioral procedure in which a biologically potent stimulus (e

    Classical conditioning

    Classical conditioning

    Classical_conditioning

  • Contrapposto
  • Sculptural disposition of human figure

    but if they did, they have not survived According to the canon of the Classical Greek sculptor Polykleitos in the 4th century BCE, contrapposto is one

    Contrapposto

    Contrapposto

    Contrapposto

  • Sigmoid function
  • Mathematical function having a characteristic S-shaped curve or sigmoid curve

    have been used as the activation function of artificial neurons. Sigmoid curves are also common in statistics as cumulative distribution functions (which

    Sigmoid function

    Sigmoid function

    Sigmoid_function

  • Supply and demand
  • Economic model of price determination in a market

    may be represented by a family of curves (with a change in the other variables constituting a shift between curves) or by a surface in a higher dimensional

    Supply and demand

    Supply and demand

    Supply_and_demand

  • Edwards curve
  • Family of elliptic curves used in cryptography

    mathematics, the Edwards curves are a family of elliptic curves studied by Harold Edwards in 2007. The concept of elliptic curves over finite fields is widely

    Edwards curve

    Edwards curve

    Edwards_curve

  • Classical guitar
  • String instrument

    The classical guitar, also known as a Spanish guitar, is a member of the guitar family used in classical music and other styles. As an acoustic wooden

    Classical guitar

    Classical guitar

    Classical_guitar

  • Kinked demand
  • Economic Model regarding demand

    initial attempt to explain sticky prices. "Kinked" demand curves and traditional demand curves are similar in that they are both downward-sloping. They

    Kinked demand

    Kinked demand

    Kinked_demand

  • David Mumford
  • American mathematician (born 1937)

    For moduli spaces, the classical idea of a "universal family of curves" would therefore be modified to a functor "of curves", with a proof that it was

    David Mumford

    David Mumford

    David_Mumford

  • Parallel curve
  • Generalization of the concept of parallel lines

    rational curves. In order to get at least rational curves, the square root of the representation of the parallel curve has to be solvable. Such curves are

    Parallel curve

    Parallel curve

    Parallel_curve

  • Brachistochrone curve
  • Fastest curve descent without friction

    which was a classical, geometrical proof, that there is only a single curve that a body can slide down in the minimum time, and that curve is the cycloid

    Brachistochrone curve

    Brachistochrone curve

    Brachistochrone_curve

  • Dose–response relationship
  • Measure of organism response to stimulus

    Dose–response relationships can be described by dose–response curves, or concentration-response curves. This is explained further in the following sections. A

    Dose–response relationship

    Dose–response relationship

    Dose–response_relationship

  • Algebraic geometry code
  • Mathematical linear code

    as the code construction was published, in their paper "Modular curves, Shimura curves, and Goppa codes, better than Varshamov-Gilbert bound". The name

    Algebraic geometry code

    Algebraic_geometry_code

  • Francis Monkman
  • English composer (1949–2023)

    English rock, classical and film score composer, and a founding member of both the progressive rock band Curved Air and the classical/rock fusion band

    Francis Monkman

    Francis Monkman

    Francis_Monkman

  • Closed timelike curve
  • World line of a particle in spacetime which returns to its starting point

    Watrous, John; Aaronson, Scott (2009). "Closed timelike curves make quantum and classical computing equivalent". Proceedings of the Royal Society A:

    Closed timelike curve

    Closed_timelike_curve

  • Envelope (mathematics)
  • Curve external to a family of curves in geometry

    is necessary that the individual members of the family of curves are differentiable curves as the concept of tangency does not apply otherwise, and there

    Envelope (mathematics)

    Envelope (mathematics)

    Envelope_(mathematics)

  • Symplectic geometry
  • Branch of differential geometry and differential topology

    pseudoholomorphic curves in symplectic geometry. Geodesics are curves of shortest length (locally), while pseudoholomorphic curves are surfaces of minimal

    Symplectic geometry

    Symplectic geometry

    Symplectic_geometry

  • Clifford Singer
  • American scholar and professor

    approaching asymptotically, circles, ellipses, hyperbolas, and many other classical curves from both ancient and modern mathematics in his works. He took part

    Clifford Singer

    Clifford Singer

    Clifford_Singer

  • Vacuum tube characteristics
  • Vacuum tube characteristics (also called tube curves, valve characteristics or valve curves) describes the electrical relationships between electrode

    Vacuum tube characteristics

    Vacuum tube characteristics

    Vacuum_tube_characteristics

  • Entasis
  • Applying convex curvature to a surface in architecture

    application of a convex curve to a surface for aesthetic purposes, or increasing strength. Its best-known use is in certain orders of Classical columns that diminish

    Entasis

    Entasis

  • Stribeck curve
  • Film lubrication versus surface friction

    Theo (2019-12-21). "Stribeck Curves" (PDF). Human Power eJournal. 11 (27). Akchurin, Aydar (2021-06-06). "Stribeck Curve". tribonet.org. Retrieved 2021-10-16

    Stribeck curve

    Stribeck_curve

  • Temporal paradox
  • Theoretical paradox resulting from time travel

    that contain closed timelike curves that lead back to the same point in spacetime, physics in or near closed timelike curves (time machines) can only be

    Temporal paradox

    Temporal_paradox

  • Stable curve
  • Asymptotically stable in the sense of geometric invariant theory

    be completely classified. One classical example of a family of stable curves is given by the Weierstrass family of curves Proj ⁡ ( Q [ t ] [ x , y , z

    Stable curve

    Stable_curve

  • Differentiable curve
  • Study of curves from a differential point of view

    Differential geometry of curves is the branch of geometry that deals with smooth curves in the plane and the Euclidean space by methods of differential

    Differentiable curve

    Differentiable_curve

  • Elliptic Curve Digital Signature Algorithm
  • Cryptographic algorithm for digital signatures

    December 15, 2017. Retrieved January 11, 2018. "SafeCurves: choosing safe curves for elliptic-curve cryptography". October 25, 2013. Archived from the

    Elliptic Curve Digital Signature Algorithm

    Elliptic_Curve_Digital_Signature_Algorithm

  • Vertex (curve)
  • Point of extreme curvature on a curve

    In the geometry of plane curves, a vertex is a point of where the first derivative of curvature is zero. This is typically a local maximum or minimum of

    Vertex (curve)

    Vertex (curve)

    Vertex_(curve)

  • Rahn curve
  • Graph of economic growth theory

    theory is used by classical liberals to argue for a decrease in overall government spending and taxation. The inverted-U-shaped curve suggests that the

    Rahn curve

    Rahn curve

    Rahn_curve

  • Gravity
  • Attraction of masses and energy

    theories of gravity or perhaps be explained in other ways. Galaxy rotation curves: Stars in galaxies follow a distribution of velocities where stars on the

    Gravity

    Gravity

    Gravity

  • History of quantum mechanics
  • Old or Older quantum theories. Building on the technology developed in classical mechanics, the invention of wave mechanics by Erwin Schrödinger and expansion

    History of quantum mechanics

    History_of_quantum_mechanics

  • Classical order
  • Styles of classical architecture, recognizable by the type of column

    Ancient Roman civilization, the architectural orders are the styles of classical architecture, each distinguished by its proportions and characteristic

    Classical order

    Classical order

    Classical_order

  • Semiclassical physics
  • Use of both classical and quantum physics to analyze a system

    theory within a classical curved gravitational background (see general relativity). Quantum chaos: quantization of classical chaotic systems. Magnetic

    Semiclassical physics

    Semiclassical_physics

  • Theory of relativity
  • Two interrelated physics theories by Albert Einstein

    due to the force of gravity as is the case in classical mechanics. This is incompatible with classical mechanics and special relativity because in those

    Theory of relativity

    Theory of relativity

    Theory_of_relativity

  • Cotes's spiral
  • Plane curve

    equations of the curves above correspond respectively to his 5 cases. The Diagram shows representative examples of the different curves. The centre is marked

    Cotes's spiral

    Cotes's_spiral

  • Area under the curve (pharmacokinetics)
  • Integral of drug concentration in blood plasma over time

    Determination of Total Area Under Glucose Tolerance and Other Metabolic Curves" purports to have independently discovered the trapezoidal rule. In Tai's

    Area under the curve (pharmacokinetics)

    Area_under_the_curve_(pharmacokinetics)

  • Contact (mathematics)
  • Two functions having equal values and derivatives at a given point

    1st-order contact if the two curves are tangent. 2nd-order contact if the curvatures of the curves are equal. Such curves are said to be osculating. 3rd-order

    Contact (mathematics)

    Contact_(mathematics)

  • Curved spacetime
  • Mathematical theory of the geometry of space and time

    ISBN 978-0-521-88705-2. Do Carmo, Manfredo P. (1976). Differential Geometry of Curves and Surfaces. Prentice-Hall. ISBN 9780132125895. Susskind, Leonard; Cabannes

    Curved spacetime

    Curved spacetime

    Curved_spacetime

  • Sponsored Content (album)
  • 2017 studio album by Antwood

    other grime works like Desert Strike (2012) by Fatima Al Qadiri and Classical Curves (2012) by Jam City. In fleshing out the album's advertising concept

    Sponsored Content (album)

    Sponsored_Content_(album)

  • Schottky group
  • the exterior of the Jordan curves defining it. The corresponding quotient space Ω(G)/G is given by joining up the Jordan curves in pairs, so is a compact

    Schottky group

    Schottky group

    Schottky_group

  • Fréchet distance
  • Measure of similarity between curves

    measure of similarity between curves that takes into account the location and ordering of the points along the curves. It is named after Maurice Fréchet

    Fréchet distance

    Fréchet_distance

  • Cygnus X-1
  • X-ray binary in Cygnus containing a stellar black hole

    Koenigsberger, G.; Peña, D.; Ruiz, E. (1995). "Spectral variations and a classical curve-of-growth analysis of HDE 226868 (Cyg X-1)". Revista Mexicana de Astronomía

    Cygnus X-1

    Cygnus X-1

    Cygnus_X-1

  • Curves Ahead
  • 1991 studio album by the Rippingtons

    allmusic.com. Retrieved March 9, 2013. The Rippingtons - Curves Ahead at AllMusic The Rippingtons - Curves Ahead at Discogs The Rippingtons Official Website

    Curves Ahead

    Curves_Ahead

  • Arabesque (ballet position)
  • Important pose of classical dance

    leg–turned out and extended behind the body, with both legs held straight. In classical ballet, an arabesque can be executed with the supporting leg en pointe

    Arabesque (ballet position)

    Arabesque (ballet position)

    Arabesque_(ballet_position)

  • Sphere
  • Set of points equidistant from a center

    unique to the sphere. All geodesics of the sphere are closed curves. Geodesics are curves on a surface that give the shortest distance between two points

    Sphere

    Sphere

    Sphere

  • Classical electromagnetism
  • Branch of theoretical physics

    Classical electromagnetism or classical electrodynamics is a branch of physics focused on the study of interactions between electric charges and currents

    Classical electromagnetism

    Classical electromagnetism

    Classical_electromagnetism

  • Neoclassical economics
  • Approach to economics

    of consumption, the derivation of demand curves for consumer goods, and the derivation of labor supply curves and reservation demand. Market analysis is

    Neoclassical economics

    Neoclassical_economics

  • Genus–degree formula
  • Theorem in classical algebraic geometry

    In classical algebraic geometry, the genus–degree formula relates the degree d {\displaystyle d} of an irreducible plane curve C {\displaystyle C} with

    Genus–degree formula

    Genus–degree_formula

  • Generalised logistic function
  • Mathematical function

    or curve is an extension of the logistic or sigmoid functions. Originally developed for growth modelling, it allows for more flexible S-shaped curves. The

    Generalised logistic function

    Generalised logistic function

    Generalised_logistic_function

  • List of contraltos in non-classical music
  • For classical and operatic singers, their voice type determines the roles they will sing and is a primary method of categorization. In classical music

    List of contraltos in non-classical music

    List_of_contraltos_in_non-classical_music

  • Modularity theorem
  • Relates rational elliptic curves to modular forms

    elliptic curves (there can also be higher-dimensional factors, so not all Hecke eigenforms correspond to rational elliptic curves). The curve obtained

    Modularity theorem

    Modularity_theorem

  • Quantum field theory in curved spacetime
  • Extension of quantum field theory to curved spacetime

    general curved spacetime. This theory uses a semi-classical approach; it treats spacetime as a fixed, classical background, while giving a quantum-mechanical

    Quantum field theory in curved spacetime

    Quantum field theory in curved spacetime

    Quantum_field_theory_in_curved_spacetime

  • Tropical geometry
  • Skeletonized version of algebraic geometry

    of divisors of tropical curves are related to chip-firing games on graphs associated to the tropical curves. Many classical theorems of algebraic geometry

    Tropical geometry

    Tropical geometry

    Tropical_geometry

  • Torelli theorem
  • Describes when a compact Riemann surface is determined by its Jacobian variety

    constructed isomorphism of the curves it follows that if the canonically principally polarized Jacobian varieties of curves of genus ≥ 2 {\displaystyle \geq

    Torelli theorem

    Torelli_theorem

  • IS–LM model
  • Macroeconomic model relating interest rates and output

    and LM curves. The LM curve may shift because of a change in monetary policy or possibly a change in inflation expectations, whereas the IS curve as in

    IS–LM model

    IS–LM model

    IS–LM_model

  • Degenerate matter
  • Type of dense exotic matter in physics

    Degenerate matter exhibits the results of Fermi-Dirac distribution. For a classical ideal gas, pressure is proportional to its temperature according to the

    Degenerate matter

    Degenerate_matter

  • 7
  • Natural number

    associations in religion, mythology, superstition and philosophy. The seven classical planets resulted in seven being the number of days in a week. 7 is often

    7

    7

  • Ancient Rome
  • Roman civilisation from the 8th century BC to the 5th century AD

    Taagepera, Rein (1979). "Size and Duration of Empires: Growth-Decline Curves, 600 B.C. to 600 A.D." Social Science History. 3 (3/4): 115–138. JSTOR 1170959

    Ancient Rome

    Ancient Rome

    Ancient_Rome

  • Franck–Condon principle
  • Quantum chemistry rule regarding vibronic transitions

    position (the minimum of potential energy) of the n curve vertically [emphasis added] upwards to the a curves in Diagram I. the particles will have a potential

    Franck–Condon principle

    Franck–Condon principle

    Franck–Condon_principle

  • Functional boxplot
  • boxplot of SST with blue curves denoting envelopes, and a black curve representing the median curve. The red dashed curves are the outlier candidates

    Functional boxplot

    Functional_boxplot

  • Vector bundles on algebraic curves
  • vector bundles on algebraic curves may be studied as holomorphic vector bundles on compact Riemann surfaces, which is the classical approach, or as locally

    Vector bundles on algebraic curves

    Vector_bundles_on_algebraic_curves

  • Darryl Way
  • English rock and classical musician (born 1948)

    Somerset, England) is an English rock and classical musician who was a founding member of the progressive rock band Curved Air and co-writer of their albums from

    Darryl Way

    Darryl_Way

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

    (For smooth curves, the geometric genus agrees with the arithmetic one.) The theorem has also been extended to general singular curves (and higher-dimensional

    Riemann–Roch theorem

    Riemann–Roch_theorem

  • Real plane curve
  • problem. See Harnack's curve theorem for a classical result. Real algebraic geometry Ragsdale conjecture "Plane real algebraic curve", Encyclopedia of Mathematics

    Real plane curve

    Real_plane_curve

  • Symmetric product of an algebraic curve
  • therefore a complex manifold. Its interest in relation to the classical geometry of curves is that its points correspond to effective divisors on C of degree n

    Symmetric product of an algebraic curve

    Symmetric_product_of_an_algebraic_curve

  • Moduli stack of elliptic curves
  • Algebraic stack in mathematics

    {\text{Spec}}(\mathbb {Z} )} classifying elliptic curves. Note that it is a special case of the moduli stack of algebraic curves M g , n {\displaystyle {\mathcal {M}}_{g

    Moduli stack of elliptic curves

    Moduli_stack_of_elliptic_curves

  • Morcom Rose Garden
  • Park in California, United States

     The Jean Street entrance on the south end welcomes visitors with a classical curved colonnade, backed by stone walls, and a rose-lined walkway, flanked

    Morcom Rose Garden

    Morcom Rose Garden

    Morcom_Rose_Garden

  • Hirzebruch–Riemann–Roch theorem
  • On the Euler characteristic of a holomorphic vector bundle on a compact complex manifold

    curves, the Hirzebruch–Riemann–Roch theorem is essentially the classical Riemann–Roch theorem. To see this, recall that for each divisor D on a curve

    Hirzebruch–Riemann–Roch theorem

    Hirzebruch–Riemann–Roch_theorem

  • Electron degeneracy pressure
  • Repulsive force in quantum mechanics

    degeneracy pressure is most prominent at low temperatures: If electrons were classical particles, the movement of the electrons would cease at absolute zero

    Electron degeneracy pressure

    Electron_degeneracy_pressure

  • Inverted yield curve
  • Phenomenon when shorter term bonds yield higher interest rates than longer term bonds

    yield curve is a yield curve in which short-term debt instruments (typically bonds) have a greater yield than longer term bonds. An inverted yield curve is

    Inverted yield curve

    Inverted yield curve

    Inverted_yield_curve

  • Jacobian variety
  • Term in mathematics

    The Jacobian of a curve over an arbitrary field was constructed by Weil (1948) as part of his proof of the Riemann hypothesis for curves over a finite field

    Jacobian variety

    Jacobian_variety

  • Algebraic geometry
  • Branch of mathematics

    hyperbolas, cubic curves like elliptic curves, and quartic curves like lemniscates and Cassini ovals. These are plane algebraic curves. A point of the plane

    Algebraic geometry

    Algebraic geometry

    Algebraic_geometry

  • Anabelian geometry
  • Theory in number theory

    arithmetic fundamental groups of two hyperbolic curves over number fields correspond to maps between the curves. A first version of Grothendieck's anabelian

    Anabelian geometry

    Anabelian_geometry

  • Hodge–Arakelov theory
  • Elliptic curves

    Hodge–Arakelov theory of elliptic curves is an analogue of classical and p-adic Hodge theory for elliptic curves carried out in the framework of Arakelov

    Hodge–Arakelov theory

    Hodge–Arakelov_theory

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