Semi-continuity of Stability for Sheaves and Variation of Gieseker Moduli Spaces
Accepted version
Peer-reviewed
Repository URI
Repository DOI
Change log
Authors
Greb, Daniel
Ross, Julius
Toma, Matei
Abstract
We investigate a semi-continuity property for stability conditions for sheaves that is important for the problem of variation of the moduli spaces as the stability condition changes. We place this in the context of a notion of stability previously considered by the authors, called multi-Gieseker-stability, that generalises the classical notion of Gieseker-stability to allow for several polarisations. As such we are able to prove that on smooth threefolds certain moduli spaces of Gieseker-stable sheaves are related by a finite number of Thaddeus-flips (that is flips arising for Variation of Geometric Invariant Theory) whose intermediate spaces are themselves moduli spaces of sheaves.
Description
Keywords
math.AG, math.AG, math.CV, math.DG, 14D20, 14J60, 32G13, 14L24, 16G20
Journal Title
Journal f\"ur die Reine und Angewandte Mathematik 749 (2019),
227-265
Conference Name
Journal ISSN
0075-4102
1435-5345
1435-5345
Volume Title
Publisher
Walter de Gruyter GmbH
Publisher DOI
Sponsorship
Engineering and Physical Sciences Research Council (EP/J002062/1)
JR is supported by an EPSRC Career Acceleration Fellowship (EP/J002062/1).