Generalized Matsushima's theorem and Kähler-Einstein cone metrics

Abstract

In this paper, we prove Matsushima's theorem for Kähler-Einstein metrics on a Fano manifold with cone singularities along a smooth divisor that is not necessarily proportional to the anti-canonical class. We then give an alternative proof of uniqueness of Kähler-Einstein cone metrics by the continuity method. Moreover, our method provides an existence theorem of Kähler-Einstein cone metrics with respect to conic Ding functional.

43 pages, title changed and typos corrected

References in corpus (2)

• Uniqueness of constant scalar curvature Kähler metrics with cone singularities, I: Reductivity
• Kähler non-collapsing, eigenvalues and the Calabi flow

Cited by in corpus (4)

• Construction of constant scalar curvature Kähler cone metrics
• Expansion formula for complex Monge-Ampère equation along cone singularities
• Existence of constant scalar curvature Kaehler cone metrics, properness and geodesic stability
• Geodesics in the space of Kahler cone metrics, II. Uniqueness of constant scalar curvature Kahler cone metrics