Classification of non-Kähler surfaces and locally conformally Kähler geometry

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-Kä...

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Bibliographic Details
Published in:Russian mathematical surveys 2021-04, Vol.76 (2), p.261-289
Main Authors: Verbitsky, M. S., Vuletescu, V., Ornea, L.
Format: Article
Language:English
Subjects:
Classification
Theorems
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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. Bibliography: 64 titles.
ISSN:0036-0279
1468-4829
DOI:10.1070/RM9858