The Serre problem is solved for fiber bundles whose fibers are two-dimensional pseudoconvex hyperbolic Reinhardt domains.
On résoud le problème de Serre pour des fibrés dont les fibres sont des domaines de Reinhardt hyperboliques pseudoconvexes de dimension deux.
Keywords: Serre problem, hyperbolic Reinhardt domains
Mot clés : problème de Serre, domaines de Reinhardt hyperboliques
Pflug, Peter 1; Zwonek, Wlodzimierz 2
@article{AIF_2004__54_1_129_0, author = {Pflug, Peter and Zwonek, Wlodzimierz}, title = {The {Serre} problem with {Reinhardt} fibers}, journal = {Annales de l'Institut Fourier}, pages = {129--146}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {54}, number = {1}, year = {2004}, doi = {10.5802/aif.2012}, zbl = {1080.32016}, mrnumber = {2069123}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.2012/} }
TY - JOUR AU - Pflug, Peter AU - Zwonek, Wlodzimierz TI - The Serre problem with Reinhardt fibers JO - Annales de l'Institut Fourier PY - 2004 SP - 129 EP - 146 VL - 54 IS - 1 PB - Association des Annales de l’institut Fourier UR - https://aif.centre-mersenne.org/articles/10.5802/aif.2012/ DO - 10.5802/aif.2012 LA - en ID - AIF_2004__54_1_129_0 ER -
%0 Journal Article %A Pflug, Peter %A Zwonek, Wlodzimierz %T The Serre problem with Reinhardt fibers %J Annales de l'Institut Fourier %D 2004 %P 129-146 %V 54 %N 1 %I Association des Annales de l’institut Fourier %U https://aif.centre-mersenne.org/articles/10.5802/aif.2012/ %R 10.5802/aif.2012 %G en %F AIF_2004__54_1_129_0
Pflug, Peter; Zwonek, Wlodzimierz. The Serre problem with Reinhardt fibers. Annales de l'Institut Fourier, Volume 54 (2004) no. 1, pp. 129-146. doi : 10.5802/aif.2012. https://aif.centre-mersenne.org/articles/10.5802/aif.2012/
[Car] Sur les transformations analytiques des domaines cerclés et semicerclés bornés, Math. Ann, Volume 106 (1932), pp. 540-573 | JFM | MR | Zbl
[Coe-Loeb] A counterexample to the Serre problem with a bounded domain in as fiber, Ann. Math., Volume 122 (1985), pp. 329-334 | MR | Zbl
[Dem] Un exemple de fibré holomorphe non de Stein à fibré ayant pour base le disque ou le plan, Invent. Math., Volume 48 (1978), pp. 293-302 | MR | Zbl
[Hir] Domains de Stein et fonctions holomorphes bornées, Math. Ann, Volume 213 (1975), pp. 185-193 | MR | Zbl
[Isa-Kra] Domains with non-compact automorphism group: a survey, Adv. Math., Volume 146 (1999), pp. 1-38 | MR | Zbl
[Kön] Über die Holomorphie-Vollständigkeit lokaltrivialer Faserräume, Math. Ann, Volume 189 (1970), pp. 178-184 | MR | Zbl
[Kru] Holomorphic automorphism of hyperbolic Reinhardt domains, Math. USSR Izv, Volume 32 (1989) no. 1, pp. 15-38 | MR | Zbl
[Loeb] Un nouveau contre-exemple a une conjecture de Serre (1984) Publ. IRMA Lille, 6(4)
[Mok] The Serre problem on Riemann surfaces, Math. Ann, Volume 258 (1981), pp. 145-168 | MR | Zbl
[Nar] Several complex variables, Chicago Lectures in Mathematics, The University of Chicago Press, Chicago-London, 1971 | MR | Zbl
[Pfl] About the Carathéodory completeness of all Reinhardt domains, Functional Analysis, Holomorphy and Approximation Theory II (1984), pp. 331-337 | MR | Zbl
[Shi] Automorphisms and equivalence of bounded Reinhardt domains not containing the origin, Tohoku Math. J., Volume 40 (1988) no. 1, pp. 119-152 | MR | Zbl
[Sib] Fibrés holomorphes et métrique de Carathéodory, C. R. Acad. Sc. Paris, Volume 279 (1974), pp. 261-264 | MR | Zbl
[Siu] Holomorphic fiber bundles whose fibers are bounded Stein domains with first Betti number, Math. Ann, Volume 219 (1976), pp. 171-192 | MR | Zbl
[Sko] Fibrés holomorphes à base fibre de Stein, Invent. Math, Volume 43 (1977), pp. 97-107 | MR | Zbl
[Ste] Fonctions plurisousharmoniques et convexité holomorphe de certaines fibrés analytiques, Séminaire Pierre Lelong (Analyse, 1973/1974) (Lecture Notes in Mathematics), Volume 474 (1975), pp. 155-179 | MR | Zbl
[Zaf] Serre problem and Inoue-Hirzebruch surfaces, Math. Ann, Volume 319 (2001) no. 2, pp. 395-420 | MR | Zbl
[Zwo1] On hyperbolicity of pseudoconvex Reinhardt domains, Arch. Math, Volume 72 (1999) no. 4, pp. 304-314 | MR | Zbl
[Zwo2] Completeness, Reinhardt domains and the method of complex geodesics in the theory of invariant functions, Diss. Math, Volume 388 (2000), pp. 1-103 | MR | Zbl
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