Relative Effective Cartier Divisor

(Algebraic Geometry)


Algebraic Geometry
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What is Relative effective Cartier divisor?

In algebraic geometry, a relative effective Cartier divisor is roughly a family of effective Cartier divisors. Precisely, an effective Cartier divisor in a scheme X over a ring R is a closed subscheme D of X that (1) is flat over R and (2) the ideal sheaf of D is locally free of rank one (i.e., invertible sheaf). Equivalently, a closed subscheme D of X is an effective Cartier divisor if there is an open affine cover of X and nonzerodivisors such that the intersection is given by the equation (called local equations) and is flat over R and such that they are compatible.

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