Semi-continuity of stability for sheaves and variation of Gieseker moduli spaces
-
Daniel Greb
,
Julius Ross
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.
Funding source: Engineering and Physical Sciences Research Council
Award Identifier / Grant number: EP/J002062/1
Funding statement: The research was supported by Engineering and Physical Sciences Research Council (Grant EP/J002062/1).
Acknowledgements
The authors wish to thank Arend Bayer for helpful conversations at a crucial stage of this project. We also thank Dominic Joyce, Jun Li, and Alexander Schmitt for discussions comparing this work to theirs. In addition, we wish to thank Ivan Smith for discussions, and also acknowledge inspiration drawn from a talk by Aaron Bertram given in January 2014 at Banff International Research Station [1].
References
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Articles in the same Issue
- Frontmatter
- Modulo p parabolic induction of pro-p-Iwahori Hecke algebra
- There are genus one curves of every index over every infinite, finitely generated field
- Kuranishi-type moduli spaces for proper CR-submersions fibering over the circle
- Petersson inner products of weight-one modular forms
- Severi varieties and Brill–Noether theory of curves on abelian surfaces
- Convergent normal form for real hypersurfaces at a generic Levi-degeneracy
- Semi-continuity of stability for sheaves and variation of Gieseker moduli spaces
- Improved bounds in Weaver and Feichtinger conjectures
- On the ramification of étale cohomology groups
Articles in the same Issue
- Frontmatter
- Modulo p parabolic induction of pro-p-Iwahori Hecke algebra
- There are genus one curves of every index over every infinite, finitely generated field
- Kuranishi-type moduli spaces for proper CR-submersions fibering over the circle
- Petersson inner products of weight-one modular forms
- Severi varieties and Brill–Noether theory of curves on abelian surfaces
- Convergent normal form for real hypersurfaces at a generic Levi-degeneracy
- Semi-continuity of stability for sheaves and variation of Gieseker moduli spaces
- Improved bounds in Weaver and Feichtinger conjectures
- On the ramification of étale cohomology groups
