Divisor (algebraic geometry)

From Citizendium
Revision as of 07:00, 8 August 2024 by Suggestion Bot (talk | contribs)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search
This article is a stub and thus not approved.
Main Article
Discussion
Related Articles  [?]
Bibliography  [?]
External Links  [?]
Citable Version  [?]
 
This editable Main Article is under development and subject to a disclaimer.

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.