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canonical divisor

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  • Canonical bundle — In mathematics, the canonical bundle of a non singular algebraic variety V of dimension n is the line bundle which is the nth exterior power of the cotangent bundle Ω on V. Over the complex numbers, it is the determinant bundle of holomorphic n… …   Wikipedia

  • Divisor (algebraic geometry) — In algebraic geometry, divisors are a generalization of codimension one subvarieties of algebraic varieties; two different generalizations are in common use, Cartier divisors and Weil divisors (named for Pierre Cartier and André Weil). These… …   Wikipedia

  • Greatest common divisor of two polynomials — Informally, the greatest common divisor (GCD) of two polynomials p ( x ) and q ( x ) is the biggest polynomial that divides evenly into both p ( x ) and q ( x ). The definition is modeled on the concept of the greatest common divisor of two… …   Wikipedia

  • Riemann–Roch theorem — In mathematics, specifically in complex analysis and algebraic geometry, the Riemann–Roch theorem is an important tool in the computation of the dimension of the space of meromorphic functions with prescribed zeroes and allowed poles. It relates… …   Wikipedia

  • Clifford's theorem on special divisors — In mathematics, Clifford s theorem on special divisors is a result of W. K. Clifford on algebraic curves, showing the constraints on special linear systems on a curve C. If D is a divisor on C, then D is (abstractly) a formal sum of points P on C …   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

  • Riemann–Roch theorem for surfaces — In mathematics, the Riemann–Roch theorem for surfaces describes the dimension of linear systems on an algebraic surface. The classical form of it was first given by Castelnuovo (1896, 1897), after preliminary versions of it were found by… …   Wikipedia

  • Noether inequality — In mathematics, the Noether inequality, named after Max Noether, is a property of compact minimal complex surfaces that restricts the topological type of the underlying topological 4 manifold. It holds more generally for minimal projective… …   Wikipedia

  • Flip (algebraic geometry) — In mathematics, specifically in algebraic geometry, a flip is a certain kind of codimension 2 surgery operation arising naturally in the attempt to construct a minimal model of an algebraic variety. The minimal model program can be summarised… …   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

  • Hirzebruch–Riemann–Roch theorem — In mathematics, the Hirzebruch–Riemann–Roch theorem, named after Friedrich Hirzebruch, Bernhard Riemann, and Gustav Roch, is Hirzebruch s 1954 result contributing to the Riemann–Roch problem for complex algebraic varieties of all dimensions. It… …   Wikipedia

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