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nonsingular curve

См. также в других словарях:

  • Curve — For other uses, see Curve (disambiguation). A parabola, a simple example of a curve In mathematics, a curve (also called a curved line in older texts) is, generally speaking, an object similar to a line but which is not required to be straight.… …   Wikipedia

  • Trott curve — In real algebraic geometry, the Trott curve is the set of points ( x , y ) satisfying the degree four polynomial equation:displaystyle 144(x^4+y^4) 225(x^2+y^2)+350x^2y^2+81=0.These points form a nonsingular quartic plane curve that has genus… …   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

  • 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

  • Singular point of a curve — In geometry, a singular point on a curve is one where the curve is not given by a smooth embedding of a parameter. The precise definition of a singular point depends on the type of curve being studied. Contents 1 Algebraic curves in the plane 1.1 …   Wikipedia

  • Supersingular elliptic curve — In algebraic geometry, a branch of mathematics, supersingular elliptic curves form a certain class of elliptic curves over a field of characteristic p > 0. Elliptic curves over such fields which are not supersingular are called… …   Wikipedia

  • Harnack's curve theorem — In real algebraic geometry, Harnack s curve theorem states when a curve of degree m can have c components. For any real plane algebraic curve of degree m, the number of components c is bounded by:frac{1 ( 1)^m}{2} le c le frac{(m 1)(m… …   Wikipedia

  • Weierstrass point — In mathematics, a Weierstrass point P on a nonsingular algebraic curve C defined over the complex numbers is a point such that there are extra functions on C , with their poles restricted to P only, than would be predicted by looking at the… …   Wikipedia

  • Polynomial lemniscate — In mathematics, a polynomial lemniscate or polynomial level curve is a plane algebraic curve of degree 2n, constructed from a polynomial p with complex coefficients of degree n.For any such polynomial p and positive real number c, we may define a …   Wikipedia

  • Algebraic variety — This article is about algebraic varieties. For the term a variety of algebras , and an explanation of the difference between a variety of algebras and an algebraic variety, see variety (universal algebra). The twisted cubic is a projective… …   Wikipedia

  • Resolution of singularities — Strong desingularization of Observe that the resolution does not stop after the first blowing up, when the strict transform is smooth, but when it is simple normal crossings with the exceptional divisors. In algebraic geometry, the problem of… …   Wikipedia

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