2017/03/18 by Julien Keller, Kai Zheng
Mathematics · #Algebraic Geometry and Number Theory #Blowing up #Conic section #Constant (computer programming) #Curvature #Divisor (algebraic geometry) #Geometric Analysis and Curvature Flows #Geometry #Geometry and complex manifolds #Gravitational singularity #Holomorphic function #Manifold (fluid mechanics) #Mathematical analysis #Mathematics #Metric (unit) #Pure mathematics #Scalar curvature #math.AG #math.CV #math.DG #msc:32L05 #msc:32Q20 #msc:53C07 #msc:53C25 #msc:53C55
paper · pdf · doi:10.1112/plms.12132
published as Proc. Lond. Math. Soc. (2018) · 46 pages
arxiv created 2017/03/18 · openalex publication_date 2018/03/28 · arxiv updated 2018/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
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.