logo AFST
Codimension one foliations on complex tori
Marco Brunella
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 19 (2010) no. 2, p. 405-418

We prove a structure theorem for codimension one singular foliations on complex tori, from which we deduce some dynamical consequences.

On démontre un théorème de structure pour les feuilletages singuliers de codimension 1 sur les tores complexes, et on en déduit des conséquences dynamiques.

Received : 2009-02-17
Accepted : 2009-06-19
Published online : 2010-09-01
DOI : https://doi.org/10.5802/afst.1248
@article{AFST_2010_6_19_2_405_0,
     author = {Marco Brunella},
     title = {Codimension one foliations on complex tori},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 19},
     number = {2},
     year = {2010},
     pages = {405-418},
     doi = {10.5802/afst.1248},
     zbl = {pre05799096},
     mrnumber = {2674768},
     language = {en},
     url = {https://afst.centre-mersenne.org/item/AFST_2010_6_19_2_405_0}
}
Brunella, Marco. Codimension one foliations on complex tori. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 19 (2010) no. 2, pp. 405-418. doi : 10.5802/afst.1248. afst.centre-mersenne.org/item/AFST_2010_6_19_2_405_0/

[Bru] M. Brunella, On the dynamics of codimension one foliations with ample normal bundle, Indiana Univ. Math. J. 57 (2008), 3101–3113 | MR 2492227 | Zbl 1170.37023

[Deb] O. Debarre, Tores et variétés abéliennes complexes, Cours Spécialisés 6, SMF (1999) | MR 1767634 | Zbl 0964.14037

[Fri] R. Friedman, Algebraic surfaces and holomorphic vector bundles, Universitext, Springer (1998) | MR 1600388 | Zbl 0902.14029

[Ghy] É. Ghys, Feuilletages holomorphes de codimension un sur les espaces homogènes complexes, Ann. Fac. Sci. Toulouse Math. (6) 5 (1996), 493–519 | Numdam | MR 1440947 | Zbl 0877.57014

[Lin] A. Lins Neto, A note on projective Levi flats and minimal sets of algebraic foliations, Ann. Inst. Fourier 49 (1999), 1369–1385 | Numdam | MR 1703092 | Zbl 0963.32022

[Mas] B. Maskit, Kleinian groups, Grundlehren der Mathematischen Wissenschaften 287, Springer (1988) | MR 959135 | Zbl 0627.30039

[Ohs] T. Ohsawa, A reduction theorem for stable sets of holomorphic foliations on complex tori, preprint (2008) | MR 2552952 | Zbl 1187.32009

[Pet] Th. Peternell, Pseudoconvexity, the Levi problem and vanishing theorems, in Several Complex Variables VII, Encyclopaedia Math. Sci. 74, Springer (1994) | MR 1326622 | Zbl 0811.32011

[Suw] T. Suwa, Indices of vector fields and residues of singular holomorphic foliations, Actualités Mathématiques, Hermann (1998) | MR 1649358 | Zbl 0910.32035