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

総合政策学部

研究成果: Article › 査読

3 被引用数 (Scopus)

抄録

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.

本文言語	English
ページ（範囲）	681-706
ページ数	26
ジャーナル	Communications in Analysis and Geometry
巻	29
号	3
DOI	https://doi.org/10.4310/CAG.2021.v29.n3.a4
出版ステータス	Published - 2021

ASJC Scopus subject areas

分析
統計学および確率
幾何学とトポロジー
統計学、確率および不確実性

文献へのアクセス

10.4310/CAG.2021.v29.n3.a4

他のファイルとリンク

引用スタイル

@article{a912f9c5ed54423dbb4f1d2ff295cb99,

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",

journal = "Communications in Analysis and Geometry",

issn = "1019-8385",

publisher = "International Press, Inc.",

number = "3",

}

TY - JOUR

T1 - Weil-Petersson geometry on the space of Bridgeland stability conditions

AU - Fan, Yu Wei

AU - Kanazawa, Atsushi

AU - Yau, Shing Tung

N1 - 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: © 2021 International Press of Boston, Inc.. All rights reserved.

PY - 2021

Y1 - 2021

N2 - 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.

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.

UR - https://www.scopus.com/pages/publications/85106474017

UR - https://www.scopus.com/pages/publications/85106474017#tab=citedBy

U2 - 10.4310/CAG.2021.v29.n3.a4

DO - 10.4310/CAG.2021.v29.n3.a4

M3 - Article

AN - SCOPUS:85106474017

SN - 1019-8385

VL - 29

SP - 681

EP - 706

JO - Communications in Analysis and Geometry

JF - Communications in Analysis and Geometry

IS - 3

ER -

Weil-Petersson geometry on the space of Bridgeland stability conditions

抄録

ASJC Scopus subject areas

文献へのアクセス

他のファイルとリンク

フィンガープリント

引用スタイル