Colmatage de surfaces holomorphes et classification des surfaces compactes
Annales de l'Institut Fourier, Tome 43 (1993) no. 3, p. 713-741
On considère le problème du colmatage en dimension 2, où l’on examine sous quelle condition une hypersurface strictement pseudoconvexe dans une surface holomorphe est le bord d’un espace de Stein. On montre que l’exemple de Rossi d’une hypersurface strictement pseudoconvexe Σ, qui est le bord de deux domaines non relativement compacts, n’est jamais le bord d’un espace de Stein bien que les fonctions holomorphes définies dans un voisinage de Σ donnent des cartes locales. On démontre que dans une surface holomorphe compacte sans fonctions méromorphes vérifiant b 1 (S)=1, un tel phéomène ne peut se produire.
We consider the problem of filling in holes in dimension 2 where we examine under which condition a strictly pseudoconvex hypersurface in an analytic surface is the boundary of a Stein space. We show that Rossi’s example of a strictly pseudoconvex hypersurface Σ, which bounds two nonrelatively compact domains, is not the boundary of a Stein space although holomorphic functions in a neighbourhood of Σ give local charts. We show that in a compact complex surface S without nonconstant meromorphic functions with b 1 (S)=1, such a phenomenon cannot exist
@article{AIF_1993__43_3_713_0,
     author = {Dloussky, Georges},
     title = {Colmatage de surfaces holomorphes et classification des surfaces compactes},
     journal = {Annales de l'Institut Fourier},
     publisher = {Imprimerie Louis-Jean},
     address = {Gap},
     volume = {43},
     number = {3},
     year = {1993},
     pages = {713-741},
     doi = {10.5802/aif.1352},
     zbl = {0783.32008},
     mrnumber = {94j:32010},
     language = {fr},
     url = {http://http://www.numdam.org/item/AIF_1993__43_3_713_0}
}
Dloussky, Georges. Colmatage de surfaces holomorphes et classification des surfaces compactes. Annales de l'Institut Fourier, Tome 43 (1993) no. 3, pp. 713-741. doi : 10.5802/aif.1352. http://www.numdam.org/item/AIF_1993__43_3_713_0/

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