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Stability conditions and crepant small resolutions


Author: Yukinobu Toda
Journal: Trans. Amer. Math. Soc. 360 (2008), 6149-6178
MSC (2000): Primary 14J32, 14E30, 18E30
Published electronically: May 29, 2008
MathSciNet review: 2425708
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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.


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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

DOI: https://doi.org/10.1090/S0002-9947-08-04509-1
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
Article copyright: © Copyright 2008 American Mathematical Society