A New Criterion for Affineness. (20th March 2013)

• Record Type: Journal Article
• Authors: Zhang, Jing
• Other Names: Airault H. Academic Editor.; Dascalescu S. Academic Editor.; Jaballah A. Academic Editor.; Kelarev A. V. Academic Editor.; Rapinchuk A. Academic Editor.
• Is Part Of: ISRN algebra. Volume 2013(2013)
• Publication Date: 2013-03-20
• Subjects: Algebra -- Periodicals; Algebra; Periodicals; Electronic journals; 512
• DOI: 10.1155/2013/786576
• Languages: English
• ISSNs: 2090-6285

Abstract

Abstract : We show that an irreducible quasiprojective variety Y of dimension d ≥ 1 defined over an algebraically closed field with characteristic zero is an affine variety if and only if H i (Y,  Y ) = 0 and H i (Y,  Y ( − Z ) ) = 0 for all i > 0, Z = H ∩ Y, where H is any hypersurface with sufficiently large degree. A direct application is that an irreducible quasiprojective variety Y over ℂ is a Stein variety if it satisfies the two vanishing conditions. Here, all sheaves are algebraic.