Weil-Petersson geometry on the space of Bridgeland stability conditions

Yu-Wei Fan Atsushi Kanazawa Shing-Tung Yau

Algebraic Geometry mathscidoc:1912.43643

arXiv preprint arXiv:1708.02161, 2017.8
Inspired by mirror symmetry, we investigate some differential geometric aspects of the space of Bridgeland stability conditions on a Calabi-Yau triangulated category. The aim is to develop theory of Weil-Petersson geometry on the stringy K\" ahler moduli space. A few basic examples are studied. In particular, we identify our Weil-Petersson metric with the Bergman metric on a Siegel modular variety in the case of the self-product of an elliptic curve.
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@inproceedings{yu-wei2017weil-petersson,
  title={Weil-Petersson geometry on the space of Bridgeland stability conditions},
  author={Yu-Wei Fan, Atsushi Kanazawa, and Shing-Tung Yau},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204701604438207},
  booktitle={arXiv preprint arXiv:1708.02161},
  year={2017},
}
Yu-Wei Fan, Atsushi Kanazawa, and Shing-Tung Yau. Weil-Petersson geometry on the space of Bridgeland stability conditions. 2017. In arXiv preprint arXiv:1708.02161. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224204701604438207.
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