A characterization of Inoue-Hirzebruch surfaces

Karl Oeljeklaus[1]; Matei Toma[2]; Dan Zaffran[1]

  • [1] Centre de Mathématiques et d'Informatique, LATP-UMR 6632, 39 rue Joliot-Curie, 13453 Marseille Cedex 13
  • [2] Universität Osnabrück, Fachbereich Mathematik-Informatik, 49069 Osnabrück

Annales de l’institut Fourier (2001)

  • Volume: 51, Issue: 5, page 1243-1257
  • ISSN: 0373-0956

Abstract

top
We show that among the surfaces of class V I I 0 with b 2 > 0 , the Inoue-Hirzebruch surfaces are characterized by the property of admitting two twisted vector fields. This result is a step towards the understanding of foliations on V I I 0 surfaces.

How to cite

top

Oeljeklaus, Karl, Toma, Matei, and Zaffran, Dan. "Une caractérisation des surfaces d'Inoue-Hirzebruch." Annales de l’institut Fourier 51.5 (2001): 1243-1257. <http://eudml.org/doc/115947>.

@article{Oeljeklaus2001,
abstract = {On montre que parmi les surfaces compactes complexes de classe $VII_0$ avec $b_2&gt;0$, les surfaces d’Inoue-Hirzebruch sont caractérisées par le fait qu’elles possèdent deux champs de vecteurs tordus. Ce résultat est un pas vers la compréhension des feuilletages sur les surfaces $VII_0$.},
affiliation = {Centre de Mathématiques et d'Informatique, LATP-UMR 6632, 39 rue Joliot-Curie, 13453 Marseille Cedex 13; Universität Osnabrück, Fachbereich Mathematik-Informatik, 49069 Osnabrück; Centre de Mathématiques et d'Informatique, LATP-UMR 6632, 39 rue Joliot-Curie, 13453 Marseille Cedex 13},
author = {Oeljeklaus, Karl, Toma, Matei, Zaffran, Dan},
journal = {Annales de l’institut Fourier},
keywords = {compact complex surface; class seven (VII); Inoue-Hirzebruch; holomorphic singular foliation; elliptic singularity},
language = {fre},
number = {5},
pages = {1243-1257},
publisher = {Association des Annales de l'Institut Fourier},
title = {Une caractérisation des surfaces d'Inoue-Hirzebruch},
url = {http://eudml.org/doc/115947},
volume = {51},
year = {2001},
}

TY - JOUR
AU - Oeljeklaus, Karl
AU - Toma, Matei
AU - Zaffran, Dan
TI - Une caractérisation des surfaces d'Inoue-Hirzebruch
JO - Annales de l’institut Fourier
PY - 2001
PB - Association des Annales de l'Institut Fourier
VL - 51
IS - 5
SP - 1243
EP - 1257
AB - On montre que parmi les surfaces compactes complexes de classe $VII_0$ avec $b_2&gt;0$, les surfaces d’Inoue-Hirzebruch sont caractérisées par le fait qu’elles possèdent deux champs de vecteurs tordus. Ce résultat est un pas vers la compréhension des feuilletages sur les surfaces $VII_0$.
LA - fre
KW - compact complex surface; class seven (VII); Inoue-Hirzebruch; holomorphic singular foliation; elliptic singularity
UR - http://eudml.org/doc/115947
ER -

References

top
  1. M. Brunella, Feuilletages holomorphes sur les surfaces complexes compactes, Ann. Sci. École Norm. Sup. (4) 30 (1997), 569-594 Zbl0893.32019MR1474805
  2. G. Dloussky, Une construction élémentaire des surfaces d'Inoue-Hirzebruch, Math. Ann. 280 (1988), 663-682 Zbl0617.14025MR939925
  3. G. Dloussky, K. Oeljeklaus, Vector fields and foliations on compact surfaces of class V I I 0 , Ann. Inst. Fourier 43 (1999), 1503-1545 Zbl0978.32021MR1723825
  4. G. Dloussky, K. Oeljeklaus, M. Toma, Surfaces de la classe V I I 0 admettant un champ de vecteurs, Comment. Math. Helv. 75 (2000), 255-270 Zbl0984.32009MR1774705
  5. G. Dloussky, K. Oeljeklaus, M. Toma, Surfaces de la classe V I I 0 admettant un champ de vecteurs, II Zbl1011.32014MR1881701
  6. D. Eisenbud, Commutative algebra, (1995), Springer, New York Zbl0819.13001MR1322960
  7. I. Enoki, Surfaces of class V I I 0 with curves, Tohoku Math. J., II Ser. 33 (1981), 453-492 Zbl0476.14013MR643229
  8. J. Hausen, Zur Klassifikation glatter kompakter C * -Flächen, Math. Ann. 301 (1995), 763-769 Zbl0830.32012MR1326767
  9. Ma. Kato, Compact complex manifolds containing "global" spherical shells. I, Proceedings of the International Symposium on Algebraic Geometry (Kyoto Univ., Kyoto, 1977) (1977), 45-84, Kinokuniya Book Store, Tokyo Zbl0421.32010
  10. Ma. Kato, Riemann-Roch theorem for strongly pseudoconvex manifolds of dimension 2, Math. Ann. 222 (1976), 243-250 Zbl0344.32020MR412468
  11. I. Nakamura, On surfaces of class V I I 0 with curves, Invent. Math. 78 (1984), 393-443 Zbl0575.14033MR768987
  12. I. Nakamura, On surfaces of class V I I 0 with curves. II, Tôhoku Math. J. (2) 42 (1990), 475-516 Zbl0732.14019MR1076173
  13. A. Némethi, `Weakly' elliptic Gorenstein singularities of surfaces, Invent. Math. 137 (1999), 145-167 Zbl0934.32018MR1703331
  14. J. Potters, On almost homogeneous compact complex analytic surfaces, Invent. Math. 8 (1969), 244-266 Zbl0205.25102MR259166
  15. D. van Straten, J. Steenbrink, Extendability of holomorphic differential forms near isolated hypersurface singularities, Abh. Math. Sem. Univ. Hamburg 55 (1985), 97-110 Zbl0584.32018MR831521
  16. P. Wagreich, Elliptic singularities of surfaces, Amer. J. Math. 92 (1970), 419-454 Zbl0204.54501MR291170

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.