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Effective Cartier Divisor

An effective Cartier divisor on a scheme X is a closed subscheme D whose ideal sheaf I_D is an invertible sheaf. Equivalently, locally on X, the subscheme D is cut out by one element that is not a zero divisor (Stacks Project 2026).

Effective Cartier divisors are the effective members of the group of Cartier divisors.

See also

Cartier Divisor, Ideal Sheaf, Invertible Sheaf, Subscheme, Zero Divisor

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References

Hartshorne, R. Algebraic Geometry. New York: Springer-Verlag, 1977.The Stacks Project Authors. "Effective Cartier Divisors." §31.14 in The Stacks Project, Tag 01WQ, 2026. https://stacks.math.columbia.edu/tag/01WQ.

Cite this as:

Weisstein, Eric W. "Effective Cartier Divisor." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/EffectiveCartierDivisor.html

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