Stability conditions and Calabi–Yau fibrations

Toda, Yukinobu

doi:10.1090/S1056-3911-08-00511-0

Author: Yukinobu Toda
Journal: J. Algebraic Geom. 18 (2009), 101-133
DOI: https://doi.org/10.1090/S1056-3911-08-00511-0
Published electronically: April 23, 2008
MathSciNet review: 2448280
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Abstract | References | Additional Information

Abstract: In this paper, we describe the spaces of stability conditions for the triangulated categories associated to three-dimensional Calabi–Yau fibrations. We deal with two cases, the flat elliptic fibrations and smooth $K3$ (Abelian) fibrations. In the first case, we will see that there exist chamber structures similar to those of the movable cone used in birational geometry. In the second case, we will compare the space with the space of stability conditions for the closed fiber of the fibration.

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Additional Information

Yukinobu Toda
Affiliation: Graduate School of Mathematical Sciences, University of Tokyo, 3-8-1, Komaba, Meguro, Tokyo, 153-8914, Japan
Address at time of publication: Institute for the Physics and Mathematics of the Universe, University of Tokyo, 5-1-5 Kashiwa-no-Ha, Kashiwa-City, Chiba, 277-8568, Japan
Email: toda@ms.u-tokyo.ac.jp

Received by editor(s): October 11, 2006
Received by editor(s) in revised form: September 30, 2007
Published electronically: April 23, 2008
Additional Notes: The author is supported by the Japan Society for the Promotion of Sciences Research Fellowships for Young Scientists, No. 1611452.