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Uspekhi Mat. Nauk, 2021 Volume 76, Issue 2(458), Pages 71–102 (Mi rm9858)

This article is cited in 5 papers

Classification of non-Kähler surfaces and locally conformally Kähler geometry

M. S. Verbitskyab, V. Vuletescuc, L. Orneacd

a Instituto Nacional de Matemática Pura e Aplicada (IMPA), Rio de Janeiro, Brasil
b National Research University Higher School of Economics
c University of Bucharest, Bucharest, Romania
d Institute of Mathematics "Simion Stoilow" of the Romanian Academy, Bucharest, Romania

Abstract: 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.
Bibliography: 64 titles.

Keywords: locally conformally Kähler surface, Kato surface, elliptic fibration.

UDC: 515.173.4+515.174.5

MSC: Primary 32H15; Secondary 32Q57, 53C56

Received: 30.03.2019

DOI: 10.4213/rm9858


 English version:
Russian Mathematical Surveys, 2021, 76:2, 261–289

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© Steklov Math. Inst. of RAS, 2025