Construction of constant scalar curvature Kähler cone metrics
arXiv:1703.06312 · doi:10.1112/plms.12132
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
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- 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