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invariant curve

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  • Classical modular curve — In number theory, the classical modular curve is an irreducible plane algebraic curve given by an equation Φn(x, y)=0, where for the j invariant j(τ), x=j(n τ), y=j(τ) is a point on the curve. The curve is sometimes called X0(n), though often… …   Wikipedia

  • Geometric invariant theory — In mathematics Geometric invariant theory (or GIT) is a method for constructing quotients by group actions in algebraic geometry, used to construct moduli spaces. It was developed by David Mumford in 1965, using ideas from the paper… …   Wikipedia

  • Algebraic curve — In algebraic geometry, an algebraic curve is an algebraic variety of dimension one. The theory of these curves in general was quite fully developed in the nineteenth century, after many particular examples had been considered, starting with… …   Wikipedia

  • J-invariant — nome q on the unit diskIn mathematics, Klein s j invariant, regarded as a function of a complex variable tau;, is a modular function defined on the upper half plane of complex numbers. We can express it in terms of Jacobi s theta functions, in… …   Wikipedia

  • Casson invariant — In 3 dimensional topology, a part of the mathematical field of geometric topology, the Casson invariant is an integer valued invariant of oriented integral homology 3 spheres, introduced by Andrew Casson.Kevin Walker (1992) found an extension to… …   Wikipedia

  • Gromov–Witten invariant — In mathematics, specifically in symplectic topology and algebraic geometry, Gromov–Witten (GW) invariants are rational numbers that, in certain situations, count pseudoholomorphic curves meeting prescribed conditions in a given symplectic… …   Wikipedia

  • Circular algebraic curve — In geometry, a circular algebraic curve is a type of plane algebraic curve determined by an equation F(x, y) = 0, where F is a polynomial with real coefficients and the highest order terms of F form a polynomial divisible by… …   Wikipedia

  • Elliptic curve — In mathematics, an elliptic curve is a smooth, projective algebraic curve of genus one, on which there is a specified point O . An elliptic curve is in fact an abelian variety mdash; that is, it has a multiplication defined algebraically with… …   Wikipedia

  • Plane curve — In mathematics, a plane curve is a curve in a Euclidean plane (cf. space curve). The most frequently studied cases are smooth plane curves (including piecewise smooth plane curves), and algebraic plane curves. A smooth plane curve is a curve in a …   Wikipedia

  • Pseudoholomorphic curve — In mathematics, specifically in topology and geometry, a pseudoholomorphic curve (or J holomorphic curve) is a smooth map from a Riemann surface into an almost complex manifold that satisfies the Cauchy Riemann equation. Introduced in 1985 by… …   Wikipedia

  • Bean curve — The bean curve is a quartic plane curve with the equation::x^4+x^2y^2+y^4=x(x^2+y^2) ,It is not the same as another curve also called the bean curve, or crooked egg curve, but both curves belong to a family of similar bean shaped curves.The bean… …   Wikipedia

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