Keller, Julien and Zheng, Kai (2018) Construction of constant scalar curvature Kähler cone metrics. Proceedings of the London Mathematical Society, 117 (3). pp. 527-573. doi:10.1112/plms.12132 ISSN 0024-6115 .

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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 projectivization 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.

Item Type:	Journal Article
Subjects:	Q Science > QA Mathematics
Divisions:	Faculty of Science, Engineering and Medicine > Science > Mathematics
Journal or Publication Title:	Proceedings of the London Mathematical Society
Publisher:	Cambridge University Press
ISSN:	0024-6115
Official Date:	September 2018
Dates:	Date Event September 2018 Published 28 March 2018 Available 31 January 2018 Accepted
Volume:	117
Number:	3
Page Range:	pp. 527-573
DOI:	10.1112/plms.12132
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Date of first compliant deposit:	8 February 2018
Date of first compliant Open Access:	20 June 2018

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