Semi-continuity of Stability for Sheaves and Variation of Gieseker Moduli Spaces
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Authors
Greb, Daniel
Ross, Julius
Toma, Matei
Publication Date
2019-04-01Journal Title
Journal f\"ur die Reine und Angewandte Mathematik 749 (2019),
227-265
ISSN
0075-4102
Publisher
Walter de Gruyter GmbH
Language
English
Type
Article
Metadata
Show full item recordCitation
Greb, D., Ross, J., & Toma, M. (2019). Semi-continuity of Stability for Sheaves and Variation of Gieseker
Moduli Spaces. Journal f\"ur die Reine und Angewandte Mathematik 749 (2019),
227-265 https://doi.org/10.1515/crelle-2016-0022
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.
Keywords
Gieseker stability, variation of moduli spaces, chamber structures, moduli of quiver representations, semistable sheaves on Kähler manifolds
Sponsorship
JR is supported by an EPSRC Career Acceleration Fellowship (EP/J002062/1).
Funder references
Engineering and Physical Sciences Research Council (EP/J002062/1)
Identifiers
External DOI: https://doi.org/10.1515/crelle-2016-0022
This record's URL: https://www.repository.cam.ac.uk/handle/1810/255920
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