Communications in Analysis and Geometry

Volume 29 (2021)

Number 3

Weil–Petersson geometry on the space of Bridgeland stability conditions

Pages: 681 – 706

DOI: https://dx.doi.org/10.4310/CAG.2021.v29.n3.a4

Authors

Yu-Wei Fan (Department of Mathematics, University of California, Berkeley, Calif., U.S.A.)

Atsushi Kanazawa (Faculty of Policy Management, Keio University, Fujisawa, Kanagawa, Japan)

Shing-Tung Yau (Department of Mathematics, Harvard University, Cambridge, Massachusetts, U.S.A.)

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.

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Received 21 December 2017

Accepted 4 December 2018

Published 10 May 2021