On the Kummer construction for Kcsc metrics

Abstract

Given a compact constant scalar curvature Kaehler orbifold, with nontrivial holomorphic vector fields, whose singularities admit a local ALE Kaehler Ricci-flat resolution, we find sufficient conditions on the position of the singular points to ensure the existence of a global constant scalar curvature Kaehler desingularization. This generalizes the results previously obtained by the first author with F. Pacard. A series of explicit examples is discussed.

This paper, together with the previous one by the same authors, contains more general results than arXiv:1402.5919 (by the same authors), which will then be withdrawn