The Serre problem with Reinhardt fibers

Peter Pflug[1]; Wlodzimierz Zwonek[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)

Annales de l’institut Fourier (2004)

  • Volume: 54, Issue: 1, page 129-146
  • ISSN: 0373-0956

Abstract

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

How to cite

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Pflug, Peter, and Zwonek, Wlodzimierz. "The Serre problem with Reinhardt fibers." Annales de l’institut Fourier 54.1 (2004): 129-146. <http://eudml.org/doc/116101>.

@article{Pflug2004,
abstract = {The Serre problem is solved for fiber bundles whose fibers are two-dimensional pseudoconvex hyperbolic Reinhardt domains.},
affiliation = {Carl von Ossietzky Universität Oldenburg, Fachbereich Mathematik, Postfach 2503, 26111 Oldenburg (Allemagne); Uniwersytet Jagiellonski, Instytut Matematyki, Reymonta 4, 30-059 Kraków (Pologne)},
author = {Pflug, Peter, Zwonek, Wlodzimierz},
journal = {Annales de l’institut Fourier},
keywords = {Serre problem; hyperbolic Reinhardt domains},
language = {eng},
number = {1},
pages = {129-146},
publisher = {Association des Annales de l'Institut Fourier},
title = {The Serre problem with Reinhardt fibers},
url = {http://eudml.org/doc/116101},
volume = {54},
year = {2004},
}

TY - JOUR
AU - Pflug, Peter
AU - Zwonek, Wlodzimierz
TI - The Serre problem with Reinhardt fibers
JO - Annales de l’institut Fourier
PY - 2004
PB - Association des Annales de l'Institut Fourier
VL - 54
IS - 1
SP - 129
EP - 146
AB - The Serre problem is solved for fiber bundles whose fibers are two-dimensional pseudoconvex hyperbolic Reinhardt domains.
LA - eng
KW - Serre problem; hyperbolic Reinhardt domains
UR - http://eudml.org/doc/116101
ER -

References

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  3. J.-P. Demailly, Un exemple de fibré holomorphe non de Stein à fibré ℂ 2 ayant pour base le disque ou le plan, Invent. Math. 48 (1978), 293-302 Zbl0372.32012MR508989
  4. A. Hirschowitz, Domains de Stein et fonctions holomorphes bornées, Math. Ann 213 (1975), 185-193 Zbl0284.32011MR393563
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  7. N.G. Kruzhilin, Holomorphic automorphism of hyperbolic Reinhardt domains, Math. USSR Izv 32 (1989), 15-38 Zbl0663.32019MR936521
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  11. P. Pflug, About the Carathéodory completeness of all Reinhardt domains, Functional Analysis, Holomorphy and Approximation Theory II (1984), 331-337, North-Holland, Amsterdam Zbl0536.32001MR771335
  12. S. Shimizu, Automorphisms and equivalence of bounded Reinhardt domains not containing the origin, Tohoku Math. J. 40 (1988), 119-152 Zbl0646.32003MR927081
  13. N. Sibony, Fibrés holomorphes et métrique de Carathéodory, C. R. Acad. Sc. Paris 279 (1974), 261-264 Zbl0318.32029MR352550
  14. Y.T. Siu, Holomorphic fiber bundles whose fibers are bounded Stein domains with first Betti number, Math. Ann 219 (1976), 171-192 Zbl0318.32010MR390303
  15. H. Skoda, Fibrés holomorphes à base fibre de Stein, Invent. Math 43 (1977), 97-107 Zbl0365.32018MR508091
  16. J.-L. Stehlé, Fonctions plurisousharmoniques et convexité holomorphe de certaines fibrés analytiques, Séminaire Pierre Lelong (Analyse, 1973/1974) 474 (1975), 155-179, Springer, Berlin Zbl0309.32011MR399524
  17. D. Zaffran, Serre problem and Inoue-Hirzebruch surfaces, Math. Ann 319 (2001), 395-420 Zbl0978.32008MR1815117
  18. W. Zwonek, On hyperbolicity of pseudoconvex Reinhardt domains, Arch. Math 72 (1999), 304-314 Zbl0938.32003MR1678013
  19. W. Zwonek, Completeness, Reinhardt domains and the method of complex geodesics in the theory of invariant functions, Diss. Math 388 (2000), 1-103 Zbl0965.32004MR1785672

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