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.

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