Table of Contents
ISRN Algebra
Volume 2013, Article ID 786576, 5 pages
http://dx.doi.org/10.1155/2013/786576
Research Article

A New Criterion for Affineness

Department of Mathematics and Statistics, University at Albany, SUNY, Albany, NY 12222, USA

Received 10 January 2013; Accepted 31 January 2013

Academic Editors: H. Airault, S. Dascalescu, A. Jaballah, A. V. Kelarev, and A. Rapinchuk

Copyright © 2013 Jing Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We show that an irreducible quasiprojective variety of dimension defined over an algebraically closed field with characteristic zero is an affine variety if and only if ( ) = 0 and ( ) = 0 for all , , where is any hypersurface with sufficiently large degree. A direct application is that an irreducible quasiprojective variety over is a Stein variety if it satisfies the two vanishing conditions. Here, all sheaves are algebraic.