Extension of holomorphic bundles to the disc (and Serre’s Problem on Stein bundles)

Jean-Pierre Rosay[1]

  • [1] University of Wisconsin Department of Mathematics Madison WI 53706 (USA)

Annales de l’institut Fourier (2007)

  • Volume: 57, Issue: 2, page 517-523
  • ISSN: 0373-0956

Abstract

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Holomorphic bundles, with fiber ℂ n , defined on open sets in ℂ by locally constant transition automorphisms, are shown to extend to holomorphic bundles on the Riemann sphere. In particular, it allows us to give an example of a non-Stein holomorphic bundle on the unit disc, with polynomial transition automorphisms.

How to cite

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Rosay, Jean-Pierre. "Extension of holomorphic bundles to the disc (and Serre’s Problem on Stein bundles)." Annales de l’institut Fourier 57.2 (2007): 517-523. <http://eudml.org/doc/10231>.

@article{Rosay2007,
abstract = {Holomorphic bundles, with fiber $\mathbb\{C\}^n$, defined on open sets in $\mathbb\{C\}$ by locally constant transition automorphisms, are shown to extend to holomorphic bundles on the Riemann sphere. In particular, it allows us to give an example of a non-Stein holomorphic bundle on the unit disc, with polynomial transition automorphisms.},
affiliation = {University of Wisconsin Department of Mathematics Madison WI 53706 (USA)},
author = {Rosay, Jean-Pierre},
journal = {Annales de l’institut Fourier},
keywords = {Holomorphic bundles; Stein manifolds; groups of automorphisms of $\mathbb\{C\}^n$; holomorphic bundles; groups of automorphisms of },
language = {eng},
number = {2},
pages = {517-523},
publisher = {Association des Annales de l’institut Fourier},
title = {Extension of holomorphic bundles to the disc (and Serre’s Problem on Stein bundles)},
url = {http://eudml.org/doc/10231},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Rosay, Jean-Pierre
TI - Extension of holomorphic bundles to the disc (and Serre’s Problem on Stein bundles)
JO - Annales de l’institut Fourier
PY - 2007
PB - Association des Annales de l’institut Fourier
VL - 57
IS - 2
SP - 517
EP - 523
AB - Holomorphic bundles, with fiber $\mathbb{C}^n$, defined on open sets in $\mathbb{C}$ by locally constant transition automorphisms, are shown to extend to holomorphic bundles on the Riemann sphere. In particular, it allows us to give an example of a non-Stein holomorphic bundle on the unit disc, with polynomial transition automorphisms.
LA - eng
KW - Holomorphic bundles; Stein manifolds; groups of automorphisms of $\mathbb{C}^n$; holomorphic bundles; groups of automorphisms of
UR - http://eudml.org/doc/10231
ER -

References

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  6. J-P. Demailly, Différents exemples de fibrés holomorphes non de Stein, Séminaire P. Lelong, H. Skoda 1976/77 694 (1978), 15-41, L.N. in Math. Zbl0418.32011MR522471
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  8. F. Forstnerič, J. Prezelj, Oka’s principle for holomorphic bundles with sprays, Math. Ann. 317 (2000), 117-154 Zbl0964.32017MR1760671
  9. F. Forstnerič, J-P. Rosay, Approximation of biholomorphic mappings by automorphisms of ℂ n , Inven. Math. 112 (1993), 323-349 Zbl0792.32011MR1213106
  10. M. Gromov, Oka’s principle for holomorphic sections of elliptic bundles, Journal A.M.S. 2 (1989), 851-897 Zbl0686.32012MR1001851
  11. H. Jung, Über ganze birationale Transformationen der Ebene, Reine Angew. Math. 184 (1942), 161-174 Zbl0027.08503MR8915
  12. H. Skoda, Fibrés holomorphes à base et à fibre de Stein, Inven. Math. 43 (1977), 97-107 Zbl0365.32018MR508091
  13. H. Skoda, Fibrés holomorphes à base et fibre de Stein, C. R. Acad. Sci. Paris Série AB 284 (1977), 1199-1202 Zbl0353.32032MR437802

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