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.
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.
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
This publication is cited in the following 6 articles:
Liviu Ornea, Misha Verbitsky, “Balanced Metrics and Gauduchon Cone of Locally Conformally Kähler Manifolds”, International Mathematics Research Notices, 2025:3 (2025)
L. Ornea, M. Verbitsky, “Bimeromorphic geometry of LCK manifolds”, Proc. Amer. Math. Soc., 152:2 (2024), 701–707
Liviu Ornea, Misha Verbitsky, “Lee classes on LCK manifolds with potential”, Tohoku Math. J. (2), 76:1 (2024)
Liviu Ornea, Misha Verbitsky, Victor Vuletescu, “Do products of compact complex manifolds admit LCK metrics?”, Bulletin of London Math Soc, 56:2 (2024), 756
L. Ornea, M. Verbitsky, “Supersymmetry and Hodge theory on Sasakian and Vaisman manifolds”, Manuscripta Math., 170:3-4 (2023), 629–658
L. Ornea, V. Slesar, “Deformations of Vaisman manifolds”, Differ. Geom. Appl., 85 (2022), 101940, 13 pp.
Citation in format AMSBIB
Contact us: