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Locally conformally Kähler metrics on Kato surfaces

Published online by Cambridge University Press:  11 January 2016

Marco Brunella
Marco Brunella*
Affiliation:
Institut de Mathématiques de Bourgogne, – UMR 5584, 21078 Dijon, [email protected]
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Abstract

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We show that every Kato surface admits a locally conformally Kähler metric.

Keywords

32J1532Q30
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 202 , June 2011 , pp. 77 - 81
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2011

References

[Bel] Belgun, F. A., On the metric structure of non-Kähler complex surfaces, Math. Ann. 317 (2000), 1–40.Google Scholar
[Bru] Brunella, M., Locally conformally Kähler metrics on certain non-Kählerian surfaces, Math. Ann. 346 (2010), 629–639.Google Scholar
[Dlo] Dloussky, G., Structure des surfaces de Kato, Mém. Soc. Math. France (N.S.), no. 14 (1984).CrossRefGoogle Scholar
[Kat] Kato, M., “Compact complex manifolds containing ‘global’ spherical shells” in Proceedings of the International Symposium on Algebraic Geometry (Kyoto, 1977), Kinokuniya, Tokyo, 1978, 45–84.Google Scholar