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

Dieter Happel; Dan Zacharia

doi:10.1090/S0002-9939-2013-11305-5

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

Dieter Happel, Dan Zacharia

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Let Pⁿ be the projective n-space over the complex numbers. In this note we show that an indecomposable rigid coherent sheaf on Pⁿ has a trivial endomorphism algebra. This generalizes a result of Drézet for n = 2.

Original language	English (US)
Pages (from-to)	3383-3390
Number of pages	8
Journal	Proceedings of the American Mathematical Society
Volume	141
Issue number	10
DOIs	https://doi.org/10.1090/S0002-9939-2013-11305-5
State	Published - 2013

Keywords

Coherent sheaves
Exceptional objects
Exterior algebra
Projective space
Vector bundles

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/S0002-9939-2013-11305-5

Cite this

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title = "A note on sheaves without self-extensions on the projective n-space",

abstract = "Let Pn be the projective n-space over the complex numbers. In this note we show that an indecomposable rigid coherent sheaf on Pn has a trivial endomorphism algebra. This generalizes a result of Dr{\'e}zet for n = 2.",

keywords = "Coherent sheaves, Exceptional objects, Exterior algebra, Projective space, Vector bundles",

author = "Dieter Happel and Dan Zacharia",

year = "2013",

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AU - Zacharia, Dan

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AB - Let Pn be the projective n-space over the complex numbers. In this note we show that an indecomposable rigid coherent sheaf on Pn has a trivial endomorphism algebra. This generalizes a result of Drézet for n = 2.

KW - Coherent sheaves

KW - Exceptional objects

KW - Exterior algebra

KW - Projective space

KW - Vector bundles

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JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

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ER -

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

Abstract

Keywords

ASJC Scopus subject areas

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