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arXiv · 1703.06312

Construction of constant scalar curvature K\"ahler cone metrics

Julien Keller·Kai Zheng
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Abstract

Over a compact K\"ahler manifold, we provide a Fredholm alternative result for the Lichnerowicz operator associated to a K\"ahler metric with conic singularities along a divisor. We deduce several existence results of constant scalar curvature K\"ahler metrics with conic singularities: existence result under small deformations of K\"ahler 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.

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Julien Keller, Kai Zheng. 2017-03-18. Construction of constant scalar curvature K\"ahler cone metrics. https://doi.org/10.1112/plms.12132

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