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The resolution property of algebraic surfaces

Published online by Cambridge University Press:  09 November 2011

Philipp Gross*
Affiliation:
Mathematisches Institut, Heinrich-Heine-Universität, D-40225 Düsseldorf, Deutschland, Germany (email: [email protected])
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Abstract

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We prove that on separated algebraic surfaces every coherent sheaf is a quotient of a locally free sheaf. This class contains many schemes that are neither normal, reduced, quasiprojective nor embeddable into toric varieties. Our methods extend to arbitrary two-dimensional schemes that are proper over an excellent ring.

Type
Research Article
Copyright
Copyright © Foundation Compositio Mathematica 2011

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