algebraic equivalence of divisors

Let X be a surface (a two-dimensional algebraic variety).

Definition 1.
  1. 1.

    An algebraic family of effective divisors on X parametrized by a non-singularPlanetmathPlanetmath curve T is defined to be an effective Cartier divisor 𝒟 on X×T which is flat over T.

  2. 2.

    If is an algebraic family of effective divisors on X, parametrized by a non-singular curve T, and P,QT are any two closed points on T, then we say that the corresponding divisors in , DP,DQ, are prealgebraically equivalentMathworldPlanetmathPlanetmathPlanetmathPlanetmathPlanetmath.

  3. 3.

    Two (Weil) divisors D,D on X are algebraically equivalent if there is a finite sequencePlanetmathPlanetmath D=D0,D1,,Dn=D with Di and Di+1 prealgebraically equivalent for all 0i<n.

Title algebraic equivalence of divisors
Canonical name AlgebraicEquivalenceOfDivisors
Date of creation 2013-03-22 15:34:10
Last modified on 2013-03-22 15:34:10
Owner alozano (2414)
Last modified by alozano (2414)
Numerical id 4
Author alozano (2414)
Entry type Definition
Classification msc 14C20