Blowing up K\"{a}hler manifolds with constant scalar curvature II

Abstract

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 P^n and P^n x M, where M is a Kcsc compact manifold with discrete automorphism group.