Local models for conical Kähler-Einstein metrics

Abstract

In this note we use the Calabi ansatz, in the context of metrics with conical singularities along a divisor, to produce regular Calabi-Yau cones and Kähler-Einstein metrics of negative Ricci with a cuspidal point. As an application, we describe singularities and cuspidal ends of the completions of the complex hyperbolic metrics on the moduli spaces of ordered configurations of points in the projective line introduced by Thurston and Deligne-Mostow.

References in corpus (2)

• K-stability of log Fano hyperplane arrangements
• On the stability of extensions of tangent sheaves on Kähler-Einstein Fano / Calabi-Yau pairs

Cited by in corpus (3)

• Degenerated Calabi-Yau varieties with infinite components, Moduli compactifications, and limit toroidal structures
• On the construction of a complete Kahler-Einstein metric with negative scalar curvature near an isolated log-canonical singularity
• On the continuity of Weil-Petersson volumes of the moduli space weighted points on the projective line