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.

On the Kummer construction for Kcsc metrics / Arezzo, Claudio; Della Vedova, Alberto; Lena, Riccardo; Mazzieri, Lorenzo. - In: BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA. - ISSN 1972-6724. - 12:(2019), pp. 83-132. [10.1007/s40574-018-0170-4]

On the Kummer construction for Kcsc metrics

Mazzieri, Lorenzo
2019-01-01

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.
2019
Arezzo, Claudio; Della Vedova, Alberto; Lena, Riccardo; Mazzieri, Lorenzo
On the Kummer construction for Kcsc metrics / Arezzo, Claudio; Della Vedova, Alberto; Lena, Riccardo; Mazzieri, Lorenzo. - In: BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA. - ISSN 1972-6724. - 12:(2019), pp. 83-132. [10.1007/s40574-018-0170-4]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11572/222299
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