The Serre problem with Reinhardt fibers  [ Le problème de Serre avec fibres de Reinhardt ]
Annales de l'Institut Fourier, Tome 54 (2004) no. 1, pp. 129-146.

On résoud le problème de Serre pour des fibrés dont les fibres sont des domaines de Reinhardt hyperboliques pseudoconvexes de dimension deux.

The Serre problem is solved for fiber bundles whose fibers are two-dimensional pseudoconvex hyperbolic Reinhardt domains.

DOI : https://doi.org/10.5802/aif.2012
Classification : 32L05,  32A07
Mots clés : problème de Serre, domaines de Reinhardt hyperboliques
@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'institut Fourier},
     volume = {54},
     number = {1},
     year = {2004},
     doi = {10.5802/aif.2012},
     zbl = {1080.32016},
     mrnumber = {2069123},
     language = {en},
     url = {archive.numdam.org/item/AIF_2004__54_1_129_0/}
}
Pflug, Peter; Zwonek, Wlodzimierz. The Serre problem with Reinhardt fibers. Annales de l'Institut Fourier, Tome 54 (2004) no. 1, pp. 129-146. doi : 10.5802/aif.2012. http://archive.numdam.org/item/AIF_2004__54_1_129_0/

[Car] H. Cartan Sur les transformations analytiques des domaines cerclés et semicerclés bornés, Math. Ann, Volume 106 (1932), pp. 540-573 | JFM 58.0350.02 | MR 1512773 | Zbl 0004.22002

[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 808221 | Zbl 0585.32030

[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 508989 | Zbl 0372.32012

[Hir] A. Hirschowitz Domains de Stein et fonctions holomorphes bornées, Math. Ann, Volume 213 (1975), pp. 185-193 | MR 393563 | Zbl 0284.32011

[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 1706680 | Zbl 1040.32019

[Kru] N.G. Kruzhilin Holomorphic automorphism of hyperbolic Reinhardt domains, Math. USSR Izv, Volume 32 (1989) no. 1, pp. 15-38 | MR 936521 | Zbl 0663.32019

[Kön] K. Königsberger Über die Holomorphie-Vollständigkeit lokaltrivialer Faserräume, Math. Ann, Volume 189 (1970), pp. 178-184 | MR 268410 | Zbl 0203.39001

[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 641821 | Zbl 0497.32013

[Nar] R. Narasimhan Several complex variables, Chicago Lectures in Mathematics, The University of Chicago Press, Chicago-London, 1971 | MR 342725 | Zbl 0223.32001

[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 771335 | Zbl 0536.32001

[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 927081 | Zbl 0646.32003

[Sib] N. Sibony Fibrés holomorphes et métrique de Carathéodory, C. R. Acad. Sc. Paris, Volume 279 (1974), pp. 261-264 | MR 352550 | Zbl 0318.32029

[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 390303 | Zbl 0318.32010

[Sko] H. Skoda Fibrés holomorphes à base fibre de Stein, Invent. Math, Volume 43 (1977), pp. 97-107 | MR 508091 | Zbl 0365.32018

[Ste] J.-L. Stehlé; (ed. P. Lelong, P. Doulbeaut, H. Skoda) 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 399524 | Zbl 0309.32011

[Zaf] D. Zaffran Serre problem and Inoue-Hirzebruch surfaces, Math. Ann, Volume 319 (2001) no. 2, pp. 395-420 | MR 1815117 | Zbl 0978.32008

[Zwo1] W. Zwonek On hyperbolicity of pseudoconvex Reinhardt domains, Arch. Math, Volume 72 (1999) no. 4, pp. 304-314 | MR 1678013 | Zbl 0938.32003

[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 1785672 | Zbl 0965.32004