×
Kohler, Franz

Feuilletages holomorphes singuliers sur les surfaces contenant une coquille sphérique globale. (Singular holomorphic foliations on surfaces containing a global spherical shell.). (French) Zbl 0814.57022

Ann. Inst. Fourier 45, No. 1, 161-182 (1995); erratum ibid. 46, No. 2, 589 (1996).
Summary: In short, we will remember that only the Inoue-Hirzebruch and generic surfaces possess a foliation. Precisely, the Inoue-Hirzebruch surfaces possess exactly two foliations and the generic surfaces at most one. The singular locus of these foliations is the set of singular points of the union of rational curves of the surface. These rational curves are leaves outside the singular points of the foliation.

Cited in 2 Documents

MSC:

57R30 Foliations in differential topology; geometric theory
32J15 Compact complex surfaces
32S65 Singularities of holomorphic vector fields and foliations

Keywords:

generic surfaces; Inoue-Hirzebruch surfaces; singular locus; holomorphic foliations
PDF BibTeX XML Cite
\textit{F. Kohler}, Ann. Inst. Fourier 45, No. 1, 161--182 (1995; Zbl 0814.57022)
Full Text: DOI Numdam Numdam EuDML
  • logo of hbz
  • logo of WorldCat

References:

[1] [1] , , Invariant varieties through singularities of holomorphic vector fields, Annals of Math., 115 (1982), 579-595. · Zbl 0503.32007
[2] [2] , , , Champs de vecteurs holomorphes sur des surfaces complexes compactes, Math. Annalen, 204 (1973), 73-81. · Zbl 0242.14008
[3] [3] , mémoire de la S.M.F., Structure des surfaces de Kato, tome 112, n° 14 (1984). · Zbl 0543.32012
[4] [4] , Une construction élémentaire des surfaces d’Inoue-Hirzebruch, Math. Ann., 280 (1988), 663-682. · Zbl 0617.14025
[5] [5] , Singularité d’équations différentielles, Astérisque, n° 150-151 (1987).
[6] [6] , Compact complex manifolds Containing global spherical shells I, Proc. Internat. Sympos. Algebraic Geometry (Nagota, ed) Kyoto (1977), Kinokuniya p.45-84. · Zbl 0421.32010
[7] [7] , , Holonomie et intégrale premières, Annales de l’Ecole Normale Supérieure, tome 13, n° 4 (1980), 469-523. · Zbl 0458.32005
[8] [8] , Towards classification of non-kählerian complex surfaces, Sugaku Expositions, 2 (1989), 209-229. · Zbl 0685.14020
[9] [9] , Unfoldings of complex analytic foliations with singularities. Japan. J. Math., Vol 9, n° 1 (1983). · Zbl 0591.32020
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.