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The resolution property of algebraic surfaces

Part of: Surfaces and higher-dimensional varieties Cycles and subschemes (Co)homology theory

Published online by Cambridge University Press:  09 November 2011

Philipp Gross
Philipp Gross*
Affiliation:
Mathematisches Institut, Heinrich-Heine-Universität, D-40225 Düsseldorf, Deutschland, Germany (email: gross@math.uni-duesseldorf.de)
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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.

Keywords

enough locally freesresolution propertyglobal resolutionsvector bundlessingular surfacesnon-projective surfacesgluing schemesdivisorial schemesAF-schemesquasiprojective open subsets

MSC classification

Secondary: 14F05: Sheaves, derived categories of sheaves and related constructions 14J60: Vector bundles on surfaces and higher-dimensional varieties, and their moduli 14C20: Divisors, linear systems, invertible sheaves
Type
Research Article
Information
Compositio Mathematica , Volume 148 , Issue 1 , January 2012 , pp. 209 - 226
Copyright
Copyright © Foundation Compositio Mathematica 2011

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