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Construction of constant scalar curvature K\"ahler cone metrics
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.Comment: 46 page
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