Un complément à l’article de Dloussky sur le colmatage des surfaces holomorphes
[A complement to a paper by Dloussky on filling of holomorphic surfaces]
Annales de l'Institut Fourier, Volume 58 (2008) no. 5, pp. 1723-1732.

We study compact complex surfaces which are degenerations of blown-up Hopf surfaces. We prove that if such a surface S contains a strictly pseudoconvex global real hypersurface, then S is a Kato surface. This allows to improve a result by Dloussky, published in this journal in 1993.

Nous étudions les surfaces complexes compactes qui sont des dégénérations de surfaces de Hopf éclatées. Nous démontrons que si une telle surface S contient une hypersurface réelle globale strictement pseudoconvexe, alors S est une surface de Kato. Ceci permet d’améliorer un résultat de Dloussky, paru dans ce même journal en 1993.

DOI: 10.5802/aif.2396
Classification: 32J15, 32V15
Mot clés : surfaces de classe VII, colmatage, hypersurfaces pseudoconvexes
Keywords: Surfaces of class VII, filling, pseudoconvex hypersurfaces
Brunella, Marco 1

1 IMB - CNRS UMR 5584 9 Avenue Savary 21078 Dijon (France)
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Brunella, Marco. Un complément à l’article de Dloussky sur le colmatage des surfaces holomorphes. Annales de l'Institut Fourier, Volume 58 (2008) no. 5, pp. 1723-1732. doi : 10.5802/aif.2396. http://www.numdam.org/articles/10.5802/aif.2396/

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