Construction of constant scalar curvature Kähler cone metrics

Abstract

Over a compact Kähler manifold, we provide a Fredholm alternative result for the Lichnerowicz operator associated to a Kähler metric with conic singularities along a divisor. We deduce several existence results of constant scalar curvature Kähler metrics with conic singularities: existence result under small deformations of Kähler classes, existence result over a Fano manifold, existence result over certain ruled manifolds. In this last case, we consider the projectivisation of a parabolic stable holomorphic bundle. This leads us to prove that the existing Hermitian-Einstein metric on this bundle enjoys a regularity property along the divisor on the base.

46 pages

References in corpus (2)

• On the existence of constant scalar curvature Kähler metric: a new perspective
• Schauder estimates for equations with cone metrics, I

Cited by in corpus (3)

• 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
• ALE Calabi-Yau metrics with conical singularities along a compact divisor