Kähler metrics with cone singularities along a divisor of bounded Ricci curvature

Abstract

Let $D$ be a smooth divisor in a compact complex manifold $X$ and let $\beta \in (0,1)$. We show that in any positive co-homology class on $X$ there is a Kähler metric with cone angle $2\pi \beta$ along $D$ which has bounded Ricci curvature. We use this result together with the Aubin-Yau continuity method to give an alternative proof of a well-known existence theorem for Kahler-Einstein metrics with cone singularities.

Cited by in corpus (2)

• Geodesics in the space of Kahler cone metrics, II. Uniqueness of constant scalar curvature Kahler cone metrics
• ALE Calabi-Yau metrics with conical singularities along a compact divisor