LCK metrics on complex spaces with quotient singularities

Ionita, George-Ionut; Preda, Ovidiu (2020). LCK metrics on complex spaces with quotient singularities. Manuscripta mathematica, 162(3-4), pp. 483-491. Springer-Verlag 10.1007/s00229-019-01141-w

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In this article we introduce a generalization of locally conformally Kähler metrics from complex manifolds to complex analytic spaces with singularities and study which properties of locally conformally Kähler manifolds still hold in this new setting. We prove that if a complex analytic space has only quotient singularities, then it admits a locally conformally Kähler metric if and only if its universal cover admits a Kähler metric such that the deck automorphisms act by
homotheties of the Kähler metric. We also prove that the blow-up at a point of an LCK complex space is also LCK.

Item Type:

Journal Article (Original Article)

Division/Institute:

08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematics

UniBE Contributor:

Ionita, George-Ionut

Subjects:

500 Science > 510 Mathematics

ISSN:

0025-2611

Publisher:

Springer-Verlag

Language:

English

Submitter:

Sebastiano Don

Date Deposited:

10 Feb 2021 17:34

Last Modified:

10 Feb 2021 17:34

Publisher DOI:

10.1007/s00229-019-01141-w

ArXiv ID:

1904.07119

Uncontrolled Keywords:

32C15, 53C55

BORIS DOI:

10.48350/151271

URI:

https://boris.unibe.ch/id/eprint/151271

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