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.
ASJC Scopus subject areas
- Statistics and Probability
- Geometry and Topology
- Statistics, Probability and Uncertainty