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2016 Variation of Gieseker moduli spaces via quiver GIT
Daniel Greb, Julius Ross, Matei Toma
Geom. Topol. 20(3): 1539-1610 (2016). DOI: 10.2140/gt.2016.20.1539

Abstract

We introduce a notion of stability for sheaves with respect to several polarisations that generalises the usual notion of Gieseker stability. Under a boundedness assumption which we show to hold on threefolds or for rank two sheaves on base manifolds of arbitrary dimension, we prove that semistable sheaves have a projective coarse moduli space that depends on a natural stability parameter. We then give two applications of this machinery. First, we show that given a real ample class ω N1(X) on a smooth projective threefold X there exists a projective moduli space of sheaves that are Gieseker semistable with respect to ω. Second, we prove that given any two ample line bundles on X the corresponding Gieseker moduli spaces are related by Thaddeus flips.

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Daniel Greb. Julius Ross. Matei Toma. "Variation of Gieseker moduli spaces via quiver GIT." Geom. Topol. 20 (3) 1539 - 1610, 2016. https://doi.org/10.2140/gt.2016.20.1539

Information

Received: 26 September 2014; Revised: 5 June 2015; Accepted: 3 July 2015; Published: 2016
First available in Project Euclid: 16 November 2017

zbMATH: 06624253
MathSciNet: MR3523063
Digital Object Identifier: 10.2140/gt.2016.20.1539

Subjects:
Primary: 14D20, 14J60, 32G13
Secondary: 14L24, 16G20

Rights: Copyright © 2016 Mathematical Sciences Publishers

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Vol.20 • No. 3 • 2016
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