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This article is cited in 5 scientific papers (total 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.
Received: 30.03.2019
Citation:
M. S. Verbitsky, V. Vuletescu, L. Ornea, “Classification of non-Kähler surfaces and locally conformally Kähler geometry”, Uspekhi Mat. Nauk, 76:2(458) (2021), 71–102; Russian Math. Surveys, 76:2 (2021), 261–289
Linking options:
https://www.mathnet.ru/eng/rm9858https://doi.org/10.1070/RM9858 https://www.mathnet.ru/eng/rm/v76/i2/p71
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Abstract page: | 425 | Russian version PDF: | 131 | English version PDF: | 73 | Russian version HTML: | 139 | References: | 49 | First page: | 18 |
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