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irreducible curve

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  • 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

  • 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

  • Modular curve — In number theory and algebraic geometry, a modular curve Y(Γ) is a Riemann surface, or the corresponding algebraic curve, constructed as a quotient of the complex upper half plane H by the action of a congruence subgroup Γ of the modular group of …   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

  • Cubic plane curve — A selection of cubic curves. See information page for details. Cubic curve redirects here. For information on polynomial functions of degree 3, see Cubic function. In mathematics, a cubic plane curve is a plane algebraic curve C defined by a… …   Wikipedia

  • Coble curve — In algebraic geometry, a Coble curve is an irreducible degree 6 planar curve with 10 double points. They were studied by Arthur Coble (1919, 1982). See also Coble surface References Coble, Arthur B. (1919), The Ten Nodes of the Rational… …   Wikipedia

  • Rational surface — In algebraic geometry, a branch of mathematics, a rational surface is a surface birationally equivalent to the projective plane, or in other words a rational variety of dimension two. Rational surfaces are the simplest of the 10 or so classes of… …   Wikipedia

  • Degenerate conic — Main article: Conic section In mathematics, a degenerate conic is a conic (degree 2 plane curve, the zeros of a degree 2 polynomial equation, a quadratic) that fails to be an irreducible curve. This can happen in two ways: either it is a… …   Wikipedia

  • Cone of curves — In mathematics, the cone of toot (sometimes the Kleiman Mori cone) of an algebraic variety X is a combinatorial invariant of much importance to the birational geometry of X. Contents 1 Definition 2 Applications 3 …   Wikipedia

  • Ample line bundle — In algebraic geometry, a very ample line bundle is one with enough global sections to set up an embedding of its base variety or manifold M into projective space. An ample line bundle is one such that some positive power is very ample. Globally… …   Wikipedia

  • Base locus — In mathematics, specifically algebraic geometry, the base locus of a linear system of divisors on a variety refers to the subvariety of points common to all divisors in the linear system.More precisely, suppose that [D] is a linear system of… …   Wikipedia

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