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Russian Mathematical Surveys, 2021, Volume 76, Issue 2, Pages 261–289
DOI: https://doi.org/10.1070/RM9858 (Mi rm9858) 		 
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
English version PDF (731 kB) Citations (5) Russian version article
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DOI: https://doi.org/10.1070/RM9858
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.
Funding agency Grant number
Unitatea Executiva pentru Finantarea Invatamantului Superior, a Cercetarii, Dezvoltarii si Inovarii, Romania PN-III-P4-ID-PCE-2016-0065
National Council for Scientific and Technological Development (CNPq) 313608/2017-2
The second and third authors were partially supported by a grant of the Ministry of Research and Innovation of Romania (CNCS-UEFISCDI, project no. PN-III-P4-ID-PCE-2016-0065 within the programme PNCDI III). The first author was supported by the programme NPq-Process 313608/2017-2.
Received: 30.03.2019
Bibliographic databases:
Document Type: Article
UDC: 515.173.4+515.174.5
MSC: Primary 32H15; Secondary 32Q57, 53C56
Language: English
Original paper language: Russian
Citation: M. S. Verbitsky, V. Vuletescu, L. Ornea, “Classification of non-Kähler surfaces and locally conformally Kähler geometry”, Russian Math. Surveys, 76:2 (2021), 261–289
Citation in format AMSBIB
\Bibitem{VerVulOrn21}
\by M.~S.~Verbitsky, V.~Vuletescu, L.~Ornea
\paper Classification of non-K\"ahler surfaces and locally conformally K\"ahler geometry
\jour Russian Math. Surveys
\yr 2021
\vol 76
\issue 2
\pages 261--289
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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