Néron-Severi group

Definition 1.

Let $S$ be a surface (an algebraic variety of dimenion $\mathrm{2}$) defined over an algebraically closed field $k$. The Néron-Severi group of $S$, denoted by $\mathrm{NS}\mathit{}\mathrm{(}S\mathrm{)}$, is the group of Weil divisors on $S$ modulo algebraic equivalence of divisors (see parent entry).

Theorem (Néron, Severi).

The Néron-Severi group of a surface is a finitely generated abelian group.

Title	Néron-Severi group
Canonical name	NeronSeveriGroup
Date of creation	2013-03-22 15:34:13
Last modified on	2013-03-22 15:34:13
Owner	alozano (2414)
Last modified by	alozano (2414)
Numerical id	4
Author	alozano (2414)
Entry type	Definition
Classification	msc 14C20