Classification of non-Kähler surfaces and locally conformally Kähler geometry

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 f...

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Bibliographic Details
Published inRussian mathematical surveys Vol. 76; no. 2; pp. 261 - 289
Main Authors Verbitsky, M. S., Vuletescu, V., Ornea, L.
Format Journal Article
LanguageEnglish
Published London IOP Publishing 01.04.2021
Subjects
Classification
Theorems
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Summary: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.
ISSN:0036-0279
1468-4829
DOI:10.1070/RM9858