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On the Kummer construction for Kcsc metrics

Bolletino dell Unione Matematica Italiana, ISSN: 2198-2759, Vol: 12, Issue: 1-2, Page: 83-132
2019
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Article Description

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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