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Homedivisor

## Primary tabs

# divisor

A divisor $D$ on a projective nonsingular curve over an algebraically closed field is a formal sum of points $D=\sum n_{p}p$ where only finitely many of the $n_{p}\in\mathbb{Z}$ are nonzero.

The degree of a divisor $D$ is ${\rm deg}(D)=\sum n_{p}$.

Defines:

degree

Keywords:

curve

Synonym:

Weil divisor

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

14C20*no label found*

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## Comments

## Use the more general definition?

The definition of (Weil) Divisor seems a bit too specialized here, at least from an algebraic geometer's point of view. I think the more general definition of a divisor as an element of the free abelian group generated by the prime divisors would be preferable here (a la Hartshorne).