2005/04/06 by Claudio Arezzo, Frank Pacard, Arezzo, Claudio +1 · 1 citation
Mathematics · #32C17 #58E11 #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #Geometry and complex manifolds #math.AP #math.DG #msc:32C17 #msc:58E11
paper · pdf · doi:10.48550/arxiv.math/0504115
28 pages
arxiv created 2005/04/06 · openalex publication_date 2005/04/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we continue our study about the existence of Kaehler metrics of constant scalar curvature (Kcsc) on blow ups at points of compact manifolds with Kcsc metrics started in math.DG/0411522. In this second part we deal with the case of base manifolds with holomorphic vector fields and we give sufficient conditions for the position of points to be blown up to preserve the Kcsc property. These results are obtained by a gluing procedure. We give explicit examples of our construction, in particular getting optimal results in the cases of Pn and Pn x M, where M is a Kcsc compact manifold with discrete automorphism group.