Given a compact constant scalar curvature Kähler orbifold, with nontrivial holomorphic vector fields, whose singularities admit a local ALE Kähler Ricci-flat resolution, we find sufficient conditions on the position of the singular points to ensure the existence of a global constant scalar curvature Kähler desingularization. We also give complete proofs of a number of analytic results which have been used in this context by various authors. A series of explicit examples is discussed
Arezzo, C., Vedova, A., Lena, R., Mazzieri, L. (2019). On the Kummer construction for Kcsc metrics. BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA, 12(1-2), 83-132 [10.1007/s40574-018-0170-4].
On the Kummer construction for Kcsc metrics
Vedova, Alberto Della;
2019
Abstract
Given a compact constant scalar curvature Kähler orbifold, with nontrivial holomorphic vector fields, whose singularities admit a local ALE Kähler Ricci-flat resolution, we find sufficient conditions on the position of the singular points to ensure the existence of a global constant scalar curvature Kähler desingularization. We also give complete proofs of a number of analytic results which have been used in this context by various authors. A series of explicit examples is discussed
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