Vol. 8, No. 4, 2014

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ISSN: 1944-7833 (e-only)
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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
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