The derived moduli space of stable sheaves

Behrend, Kai; Ciocan-Fontanine, Ionut; Hwang, Junho; Rose, Michael

doi:10.2140/ant.2014.8.781

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The derived moduli space of stable sheaves

Kai Behrend, Ionut Ciocan-Fontanine, Junho Hwang and Michael Rose

Vol. 8 (2014), No. 4, 781–812

DOI: 10.2140/ant.2014.8.781

Abstract

We construct the derived scheme of stable sheaves on a smooth projective variety via derived moduli of finite graded modules over a graded ring. We do this by dividing the derived scheme of actions of Ciocan-Fontanine and Kapranov by a suitable algebraic gauge group. We show that the natural notion of GIT stability for graded modules reproduces stability for sheaves.

Keywords

differential graded schemes, curved differential graded Lie algebras, stable sheaves

Mathematical Subject Classification 2010

Primary: 14D20

Milestones

Received: 28 April 2010

Revised: 3 September 2012

Accepted: 21 November 2012

Published: 10 August 2014

Authors

Kai Behrend
Department of Mathematics University of British Columbia 1984 Mathematics Road Vancouver BC V6T 1Z2 Canada

Ionut Ciocan-Fontanine
School of Mathematics University of Minnesota 206 Church Street SE Minneapolis, MN 55455 United States

Junho Hwang
Department of Mathematics University of British Columbia 1984 Mathematics Road Vancouver BC V6T 1Z2 Canada

Michael Rose
Department of Mathematics University of California, Berkeley 970 Evans Hall Berkeley, CA 94720 United States

Vol. 8, No. 4, 2014