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Ornea, Liviu; Verbitsky, Misha

Bimeromorphic geometry of LCK manifolds. (English) Zbl 1533.32007

Proc. Am. Math. Soc. 152, No. 2, 701-707 (2024).
Summary: A locally conformally Kähler (LCK) manifold is a complex manifold \(M\) which has a Kähler structure on its cover, such that the deck transform group acts on it by homotheties. Assume that the Kähler form is exact on the minimal Kähler cover of \(M\). We prove that any bimeromorphic map \(M'\rightarrow M\) is in fact holomorphic; in other words, \(M\) has a unique minimal model. This can be applied to a wide class of LCK manifolds, such as the Hopf manifolds, their complex submanifolds and to OT manifolds.

MSC:

32H04 Meromorphic mappings in several complex variables
53C55 Global differential geometry of Hermitian and Kählerian manifolds

Keywords:

locally conformally Kähler; global Kähler potential; bimeromorphism; minimal model; normal variety
PDFBibTeX XMLCite
\textit{L. Ornea} and \textit{M. Verbitsky}, Proc. Am. Math. Soc. 152, No. 2, 701--707 (2024; Zbl 1533.32007)
Full Text: DOI arXiv

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