# Difference between revisions of "Divisor (algebraic geometry)"

From Citizendium

(New entry, just a stub) |
|||

(One intermediate revision by the same user not shown) | |||

Line 1: | Line 1: | ||

+ | {{subpages}} | ||

In [[geometry]] a '''divisor''' on an [[algebraic variety]] is a formal sum (with integer coefficients) of [[subvariety|subvarieties]]. | In [[geometry]] a '''divisor''' on an [[algebraic variety]] is a formal sum (with integer coefficients) of [[subvariety|subvarieties]]. | ||

## Latest revision as of 15:54, 18 February 2009

In geometry a **divisor** on an algebraic variety is a formal sum (with integer coefficients) of subvarieties.

An **effective divisor** is a sum with non-negative integer coefficients.

## Divisors on a curve

On an algebraic curve, a divisor is a formal sum of points

with *degree*

The *support* of a divisor is the set of points with non-zero coefficients in the sum.

The divisor of a function *f*, denoted or , is supported on the poles and zeroes of the function, with coefficients the degree of the pole or zero, with positive sign for zeroes and negative sign for poles. The degree of the divisor of a function is zero.