The Serre problem with Reinhardt fibers
Annales de l'Institut Fourier, Volume 54 (2004) no. 1, pp. 129-146.

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.

DOI: 10.5802/aif.2012
Classification: 32L05, 32A07
Keywords: Serre problem, hyperbolic Reinhardt domains
Mot clés : problème de Serre, domaines de Reinhardt hyperboliques

Pflug, Peter 1; Zwonek, Wlodzimierz 2

1 Carl von Ossietzky Universität Oldenburg, Fachbereich Mathematik, Postfach 2503, 26111 Oldenburg (Allemagne)
2 Uniwersytet Jagiellonski, Instytut Matematyki, Reymonta 4, 30-059 Kraków (Pologne)
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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] H. Cartan Sur les transformations analytiques des domaines cerclés et semicerclés bornés, Math. Ann, Volume 106 (1932), pp. 540-573 | JFM | MR | Zbl

[Coe-Loeb] G. Coeuré; J.-J. Loeb A counterexample to the Serre problem with a bounded domain in 2 as fiber, Ann. Math., Volume 122 (1985), pp. 329-334 | MR | Zbl

[Dem] J.-P. Demailly Un exemple de fibré holomorphe non de Stein à fibré 2 ayant pour base le disque ou le plan, Invent. Math., Volume 48 (1978), pp. 293-302 | MR | Zbl

[Hir] A. Hirschowitz Domains de Stein et fonctions holomorphes bornées, Math. Ann, Volume 213 (1975), pp. 185-193 | MR | Zbl

[Isa-Kra] A.V. Isaev; S.G. Krantz Domains with non-compact automorphism group: a survey, Adv. Math., Volume 146 (1999), pp. 1-38 | MR | Zbl

[Kön] K. Königsberger Über die Holomorphie-Vollständigkeit lokaltrivialer Faserräume, Math. Ann, Volume 189 (1970), pp. 178-184 | MR | Zbl

[Kru] N.G. Kruzhilin Holomorphic automorphism of hyperbolic Reinhardt domains, Math. USSR Izv, Volume 32 (1989) no. 1, pp. 15-38 | MR | Zbl

[Loeb] J.-J. Loeb Un nouveau contre-exemple a une conjecture de Serre (1984) Publ. IRMA Lille, 6(4)

[Mok] N. Mok The Serre problem on Riemann surfaces, Math. Ann, Volume 258 (1981), pp. 145-168 | MR | Zbl

[Nar] R. Narasimhan Several complex variables, Chicago Lectures in Mathematics, The University of Chicago Press, Chicago-London, 1971 | MR | Zbl

[Pfl] P. Pflug; G. Zapata ed About the Carathéodory completeness of all Reinhardt domains, Functional Analysis, Holomorphy and Approximation Theory II (1984), pp. 331-337 | MR | Zbl

[Shi] S. Shimizu 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] N. Sibony Fibrés holomorphes et métrique de Carathéodory, C. R. Acad. Sc. Paris, Volume 279 (1974), pp. 261-264 | MR | Zbl

[Siu] Y.T. 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] H. Skoda Fibrés holomorphes à base fibre de Stein, Invent. Math, Volume 43 (1977), pp. 97-107 | MR | Zbl

[Ste] J.-L. Stehlé; (ed. P. Lelong, P. Doulbeaut 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] D. Zaffran Serre problem and Inoue-Hirzebruch surfaces, Math. Ann, Volume 319 (2001) no. 2, pp. 395-420 | MR | Zbl

[Zwo1] W. Zwonek On hyperbolicity of pseudoconvex Reinhardt domains, Arch. Math, Volume 72 (1999) no. 4, pp. 304-314 | MR | Zbl

[Zwo2] W. Zwonek 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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