Blowing up Kahler manifolds of constant scalar curvature, II

In this paper we prove the existence of Kaehler metrics of constant scalar curvature on the blow up at finitely many points of a compact manifold that already carries a constant scalar curvature Kaehler metric. In the case where the manifold has nontrivial holomorphic vector fields with zeros, we give necessary conditions on the number and locations of the blow up points for the blow up to carry constant scalar curvature Kaehler metrics.