Classification of non-Kähler surfaces and locally conformally Kähler geometry. (English. Russian original) Zbl 1471.32023
Russ. Math. Surv. 76, No. 2, 261-289 (2021); translation from Usp. Mat. Nauk 76, No. 2, 71-102 (2021).
Summary: The Enriques-Kodaira classification treats non-Kähler surfaces as a special case within the Kodaira framework. We prove the classification results for non-Kähler complex surfaces without relying on the machinery of the Enriques-Kodaira classification, and deduce the classification theorem for non-Kähler surfaces from the Buchdahl-Lamari theorem. We also prove that all non-Kähler surfaces which are not of class VII are locally conformally Kähler.
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