PlanetMath: divisor

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divisor

(Definition)

A divisor 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 is ${\rm deg}(D) = \sum n_p$ .

"divisor" is owned by nerdy2.

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Other names:

Weil divisor

Also defines:

degree

Keywords:

curve

Attachments:: Weil divisors on schemes (Definition) by alozano
intersection divisor for a quartic (Definition) by alozano

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Cross-references: points, sum, field, algebraically closed, curve, nonsingular
There are 46 references to this entry.

This is version 3 of divisor, born on 2001-12-12, modified 2002-09-23.
Object id is 1102, canonical name is DivisorOnACurve.
Accessed 9002 times total.

Classification:

14C20 (Algebraic geometry :: Cycles and subschemes :: Divisors, linear systems, invertible sheaves)

Pending Errata and Addenda

None.

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