Moduli stacks of semistable sheaves and representations of Ext–quivers

Toda, Yukinobu

doi:10.2140/gt.2018.22.3083

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Moduli stacks of semistable sheaves and representations of Ext–quivers

Yukinobu Toda

Geometry & Topology 22 (2018) 3083–3144

DOI: 10.2140/gt.2018.22.3083

Abstract

We show that the moduli stacks of semistable sheaves on smooth projective varieties are analytic locally on their coarse moduli spaces described in terms of representations of the associated Ext–quivers with convergent relations. When the underlying variety is a Calabi–Yau $3$ –fold, our result describes the above moduli stacks as critical loci analytic locally on the coarse moduli spaces. The results in this paper will be applied to the wall-crossing formula of Gopakumar–Vafa invariants defined by Maulik and the author.

Keywords

moduli spaces of semistable sheaves, representations of quivers

Mathematical Subject Classification 2010

Primary: 14D22, 14D23

Secondary: 14D15

References

Publication

Received: 10 October 2017

Revised: 14 December 2017

Accepted: 3 February 2018

Published: 1 June 2018

Proposed: Richard Thomas

Seconded: Jim Bryan, Dan Abramovich

Authors

Yukinobu Toda
Kavli Institute for the Physics and Mathematics of the Universe University of Tokyo Kashiwa Japan

Volume 22, issue 5 (2018)