Vol. 252, No. 1, 2011

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Splitting criteria for vector bundles on higher-dimensional varieties

Parsa Bakhtary

Vol. 252 (2011), No. 1, 19–29
Abstract

We generalize Horrocks’ criterion for the splitting of vector bundles on projective space by establishing an analogous splitting criterion for vector bundles on a class of smooth complex projective varieties of dimension 4, over which every extension of line bundles splits.

Keywords
splitting, vector bundle, Horrocks’ criterion, Grothendieck–Lefschetz theorem
Mathematical Subject Classification 2000
Primary: 14J60, 14F05
Milestones
Received: 22 October 2010
Revised: 24 November 2010
Accepted: 30 November 2010
Published: 8 October 2011

Proposed: Alexander S. Merkurjev
Authors
Parsa Bakhtary
Department of Mathematics and Statistics
King Fahd University of Petroleum and Minerals
Box 1654
Dhahran 31261
Saudi Arabia
http://faculty.kfupm.edu.sa/MATH/pbakhtary