divisor class

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• 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

• Theta-divisor — In mathematics, the theta divisor Theta; is the divisor in the sense of algebraic geometry defined on an abelian variety A over the complex numbers (and principally polarized) by the zero locus of the associated Riemann theta function. It is… …   Wikipedia

• Greatest common divisor — In mathematics, the greatest common divisor (gcd), also known as the greatest common factor (gcf), or highest common factor (hcf), of two or more non zero integers, is the largest positive integer that divides the numbers without a remainder. For …   Wikipedia

• Normal crossing divisor — In algebraic geometry, normal crossing divisors are a class of divisors which generalize the smooth divisors. Intuitively they cross only in a transversal way.Let A be an algebraic variety, and Z= Z i a reduced Cartier divisor, with Z i its… …   Wikipedia

• Conjugacy class — In mathematics, especially group theory, the elements of any group may be partitioned into conjugacy classes; members of the same conjugacy class share many properties, and study of conjugacy classes of non abelian groups reveals many important… …   Wikipedia

• Common divisor — Common Com mon, a. [Compar. {Commoner}; superl. {Commonest}.] [OE. commun, comon, OF. comun, F. commun, fr. L. communis; com + munis ready to be of service; cf. Skr. mi to make fast, set up, build, Goth. gamains common, G. gemein, and E. mean low …   The Collaborative International Dictionary of English

• Conductor (class field theory) — In algebraic number theory, the conductor of a finite abelian extension of local or global fields provides a quantitative measure of the ramification in the extension. The definition of the conductor is related to the Artin map. Contents 1 Local… …   Wikipedia

• 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

• Theta characteristic — In mathematics, a theta characteristic of a non singular algebraic curve C is a divisor class Θ such that 2Θ is the canonical class, In terms of holomorphic line bundles L on a connected compact Riemann surface, it is therefore L such that L 2 is …   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

• Del Pezzo surface — In mathematics, a del Pezzo surface or Fano surface is a two dimensional Fano variety, in other words a non singular projective algebraic surface with ample anticanonical divisor class. They are in some sense the opposite of surfaces of general… …   Wikipedia