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Weil–Petersson geometry on the space of Bridgeland stability conditions
Communications in Analysis and Geometry  (IF0.736),  Pub Date : 2021-05-01, DOI: 10.4310/cag.2021.v29.n3.a4
Yu-Wei Fan, Atsushi Kanazawa, Shing-Tung Yau

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.