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A cohomological splitting criterion for locally free sheaves on arithmetically Cohen–Macaulay surfaces

Published online by Cambridge University Press:  03 July 2013

MIHAI HALIC  and
ROSHAN TAJAROD
MIHAI HALIC
Affiliation:
Department of Mathematics and Statistics, King Fahd University of Petroleum and MineralsDhahran 31261, Saudi Arabia. e-mail: mihai.halic@gmail.com
ROSHAN TAJAROD
Affiliation:
School of Mathematics, IPM, P.O. Box 19395-5746, Tehran, Iran. e-mail: roshan.tajarod@gmail.com
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Abstract

In this paper we obtain a cohomological splitting criterion for locally free sheaves on arithmetically Cohen–Macaulay surfaces with cyclic Picard group, which is similar to Horrocks' splitting criterion for locally free sheaves on projective spaces. We also recover a duality property which identifies a general K3 surface with a certain moduli space of stable sheaves on it, and obtain examples of stable, arithmetically Cohen–Macaulay, locally free sheaves of rank two on general surfaces of degree at least five in ${\mathbb P}^3$.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 155 , Issue 3 , November 2013 , pp. 517 - 527
Copyright
Copyright © Cambridge Philosophical Society 2013 

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