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Variation of Gieseker
moduli spaces via quiver GIT
Daniel Greb, Julius Ross and Matei Toma |
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Geometry & Topology 20 (2016) 1539–1610
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Abstract |
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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 on a smooth projective threefold there exists a projective moduli space of sheaves that are Gieseker semistable with respect to . Second, we prove that given any two ample line bundles on the corresponding Gieseker moduli spaces are related by Thaddeus flips. |
Keywords
Gieseker stability, variation of moduli spaces, chamber
structures, boundedness, moduli of quiver representations,
semistable sheaves on Kähler manifolds
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Mathematical Subject Classification 2010
Primary: 14D20, 14J60, 32G13
Secondary: 14L24, 16G20
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References |
Publication
Received: 26 September 2014
Revised: 5 June 2015
Accepted: 3 July 2015
Published: 4 July 2016
Proposed: Richard Thomas
Seconded: Jim Bryan, Frances Kirwan
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Authors |
| Daniel Greb | |
| Essener Seminar für Algebraische
Geometrie und Arithmetik Fakultät für Mathematik Universität Duisburg-Essen D-45117 Essen Germany |
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| Julius Ross | |
| Department of Pure Mathematics and
Mathematical Statistics Centre for Mathematical Sciences University of Cambridge Wilberforce Road Cambridge CB3 0WB UK |
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| Matei Toma | |
| Institut de Mathématiques Élie
Cartan Université de Lorraine BP 70239 54506 Vandoeuvre-lès-Nancy Cedex France |
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