We study compact complex surfaces which are degenerations of blown-up Hopf surfaces. We prove that if such a surface contains a strictly pseudoconvex global real hypersurface, then 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 contient une hypersurface réelle globale strictement pseudoconvexe, alors est une surface de Kato. Ceci permet d’améliorer un résultat de Dloussky, paru dans ce même journal en 1993.
Mot clés : surfaces de classe VII, colmatage, hypersurfaces pseudoconvexes
Keywords: Surfaces of class VII, filling, pseudoconvex hypersurfaces
@article{AIF_2008__58_5_1723_0, author = {Brunella, Marco}, title = {Un compl\'ement \`a l{\textquoteright}article de {Dloussky} sur le colmatage des surfaces holomorphes}, journal = {Annales de l'Institut Fourier}, pages = {1723--1732}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {58}, number = {5}, year = {2008}, doi = {10.5802/aif.2396}, zbl = {1149.32011}, mrnumber = {2445831}, language = {fr}, url = {http://archive.numdam.org/articles/10.5802/aif.2396/} }
TY - JOUR AU - Brunella, Marco TI - Un complément à l’article de Dloussky sur le colmatage des surfaces holomorphes JO - Annales de l'Institut Fourier PY - 2008 SP - 1723 EP - 1732 VL - 58 IS - 5 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.2396/ DO - 10.5802/aif.2396 LA - fr ID - AIF_2008__58_5_1723_0 ER -
%0 Journal Article %A Brunella, Marco %T Un complément à l’article de Dloussky sur le colmatage des surfaces holomorphes %J Annales de l'Institut Fourier %D 2008 %P 1723-1732 %V 58 %N 5 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.2396/ %R 10.5802/aif.2396 %G fr %F AIF_2008__58_5_1723_0
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://archive.numdam.org/articles/10.5802/aif.2396/
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