Weil-Petersson geometry on the space of Bridgeland stability conditions

Yu Wei Fan; Atsushi Kanazawa; Shing Tung Yau

doi:10.4310/CAG.2021.v29.n3.a4

Weil-Petersson geometry on the space of Bridgeland stability conditions

Yu Wei Fan
, Atsushi Kanazawa
, Shing Tung Yau

Faculty of Policy Management

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

We investigate some differential geometric aspects of the space of Bridgeland stability conditions on a Calabi-Yau triangulated category The aim is to give a provisional definition of Weil-Petersson geometry on the stringy Kähler moduli space. We study in detail a few basic examples to support our proposal. 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.

Original language	English
Pages (from-to)	681-706
Number of pages	26
Journal	Communications in Analysis and Geometry
Volume	29
Issue number	3
DOIs	https://doi.org/10.4310/CAG.2021.v29.n3.a4
Publication status	Published - 2021

ASJC Scopus subject areas

Analysis
Statistics and Probability
Geometry and Topology
Statistics, Probability and Uncertainty

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10.4310/CAG.2021.v29.n3.a4

Cite this

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title = "Weil-Petersson geometry on the space of Bridgeland stability conditions",

abstract = "We investigate some differential geometric aspects of the space of Bridgeland stability conditions on a Calabi-Yau triangulated category The aim is to give a provisional definition of Weil-Petersson geometry on the stringy K{\"a}hler moduli space. We study in detail a few basic examples to support our proposal. 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.",

author = "Fan, \{Yu Wei\} and Atsushi Kanazawa and Yau, \{Shing Tung\}",

note = "Funding Information: We are grateful to Shinobu Hosono, Yukinobu Toda and Jie Zhou for useful discussions. Special thanks go to Hiroshi Iritani for drawing our attention to the Gamma class. The present work was initiated when A. K. was supported by Harvard CMSA. It was supported in part by the Kyoto Hakubi Project and JSPS Grant-in-Aid Wakate(B)17K17817. Part of the work was done when Y.-W. F. was visiting Kavli IPMU and Kyoto University. The work of S.-T. Y. was supported by the Simons Collaboration Grant on Homological Mirror Symmetry 385581, NSF grant DMS-1607871, and Harvard CMSA. Publisher Copyright: {\textcopyright} 2021 International Press of Boston, Inc.. All rights reserved.",

year = "2021",

doi = "10.4310/CAG.2021.v29.n3.a4",

language = "English",

volume = "29",

pages = "681--706",

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AU - Fan, Yu Wei

AU - Kanazawa, Atsushi

AU - Yau, Shing Tung

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AB - We investigate some differential geometric aspects of the space of Bridgeland stability conditions on a Calabi-Yau triangulated category The aim is to give a provisional definition of Weil-Petersson geometry on the stringy Kähler moduli space. We study in detail a few basic examples to support our proposal. 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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JO - Communications in Analysis and Geometry

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IS - 3

ER -

Weil-Petersson geometry on the space of Bridgeland stability conditions

Abstract

ASJC Scopus subject areas

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