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A note on sheaves without self-extensions on the projective $ n$-space

Authors: Dieter Happel and Dan Zacharia
Journal: Proc. Amer. Math. Soc. 141 (2013), 3383-3390
MSC (2010): Primary 14F05, 16E10; Secondary 16E65, 16G20, 16G70
Published electronically: June 19, 2013
MathSciNet review: 3080161
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Abstract: Let $ {\bf P}^n$ be the projective $ n$-space over the complex numbers. In this note we show that an indecomposable rigid coherent sheaf on $ {\bf P}^n$ has a trivial endomorphism algebra. This generalizes a result of Drézet for $ n=2.$

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Additional Information

Dieter Happel
Affiliation: Fakultät für Mathematik, Technische Universität Chemnitz, 09107 Chemnitz, Germany

Dan Zacharia
Affiliation: Department of Mathematics, Syracuse University, Syracuse, New York 13244-0001

Keywords: Exterior algebra, projective space, coherent sheaves, vector bundles, exceptional objects
Received by editor(s): December 4, 2010
Received by editor(s) in revised form: December 20, 2011
Published electronically: June 19, 2013
Additional Notes: The second author is supported by the NSA grant H98230-11-1-0152.
Communicated by: Harm Derksen
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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