## Stability conditions and crepant small resolutions

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## Abstract:

In this paper, we describe the spaces of stability conditions on the triangulated categories associated to three dimensional crepant small resolutions. The resulting spaces have chamber structures such that each chamber corresponds to a birational model together with a special Fourier-Mukai transform. We observe that these spaces are covering spaces over certain open subsets of finite dimensional vector spaces and determine their deck transformations.## References

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## Additional Information

**Yukinobu Toda**- Affiliation: Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo, Japan
- Address at time of publication: Institute for the Physics and Mathematics of the Universe, University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa City, Chiba, Japan
- Email: toda@ms.u-tokyo.ac.jp
- Received by editor(s): October 11, 2006
- Received by editor(s) in revised form: February 26, 2007, and March 12, 2007
- Published electronically: May 29, 2008
- © Copyright 2008 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**360**(2008), 6149-6178 - MSC (2000): Primary 14J32, 14E30, 18E30
- DOI: https://doi.org/10.1090/S0002-9947-08-04509-1
- MathSciNet review: 2425708