Open Access
Translator Disclaimer
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


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.


Download Citation

Daniel Greb. Julius Ross. Matei Toma. "Variation of Gieseker moduli spaces via quiver GIT." Geom. Topol. 20 (3) 1539 - 1610, 2016.


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

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

Rights: Copyright © 2016 Mathematical Sciences Publishers


Vol.20 • No. 3 • 2016
Back to Top