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 n , defined on open sets in 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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  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 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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