The derived moduli space of stable sheaves

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

doi:10.2140/ant.2014.8.781

The derived moduli space of stable sheaves

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

School of Mathematics

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

4 Scopus citations

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.

Original language	English (US)
Pages (from-to)	781-812
Number of pages	32
Journal	Algebra and Number Theory
Volume	8
Issue number	4
DOIs	https://doi.org/10.2140/ant.2014.8.781
State	Published - 2014

Keywords

Curved differential graded lie algebras
Differential graded schemes
Stable sheaves

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10.2140/ant.2014.8.781

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title = "The derived moduli space of stable sheaves",

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 = "Curved differential graded lie algebras, Differential graded schemes, Stable sheaves",

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

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language = "English (US)",

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T1 - The derived moduli space of stable sheaves

AU - Behrend, Kai

AU - Ciocan-Fontanine, Ionut

AU - Hwang, Junho

AU - Rose, Michael

PY - 2014

Y1 - 2014

N2 - 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.

AB - 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.

KW - Curved differential graded lie algebras

KW - Differential graded schemes

KW - Stable sheaves

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DO - 10.2140/ant.2014.8.781

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JO - Algebra and Number Theory

JF - Algebra and Number Theory

IS - 4

ER -

The derived moduli space of stable sheaves

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Keywords

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