Weil-Petersson geometry on the space of Bridgeland stability conditions

2017/08/07 by Fan, Yu-Wei, Kanazawa, Atsushi, Yau, Shing-Tung · 1 citation
#14J32 #14J33 #18E30 #53D37 #Algebraic Geometry (math.AG) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th)

paper · doi:10.48550/arxiv.1708.02161

Abstract

Inspired by mirror symmetry, we investigate some differential geometric aspects of the space of Bridgeland stability conditions on a Calabi-Yau triangulated category. The aim is to develop theory of Weil-Petersson geometry on the stringy Kähler moduli space. A few basic examples are studied. 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.

Cited by

• Mirror symmetry for lattice-polarized abelian surfaces

Related

• Local and Global Aspects of Weil-Petersson Geometry
• Weil-Petersson Teichmüller theory of surfaces of infinite conformal type
• Bridgeland stability conditions on some higher-dimensional Calabi--Yau manifolds and generalized Kummer varieties
• Weil-Petersson perspectives
• Geometry of the Weil-Petersson completion of Teichmüller space