Weil-Petersson geometry on the space of Bridgeland stability conditions

摘要

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 Kahler 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.