2014/05/19 by Michael Dabkowski, Michael G. Dabkowski, Dabkowski, Michael G. +2
Mathematics · Physics and Astronomy · #32J27 #53C25 #53C55 #Advanced Differential Geometry Research #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.DG #msc:32J27 #msc:53C25 #msc:53C55
paper · pdf · doi:10.48550/arxiv.1405.4920
14 pages
openalex publication_date 2014/05/19 · arxiv created 2015/09/10 · arxiv updated 2015/09/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that a certain class of ALE spaces always has a Kahler conformal compactification, and moreover provide explicit formulas for the conformal factor and the Kahler potential of said compactification. We then apply this to give a new and simple construction of the canonical Bochner-Kähler metric on certain weighted projective spaces, and also to explicitly construct a family Kahler edge-cone metrics on \mathbbCP2, with singular set \mathbbCP1, having cone angles 2πβ for all β>0. We conclude by discussing how these results can be used to obtain certain well-known Einstein metrics.