Regular foliations on weak Fano manifolds
Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 26 (2017) no. 1, pp. 207-217.

Dans cette note, nous montrons que tout feuilletage régulier sur une variété de Fano faible est algébriquement intégrable.

In this paper we prove that a regular foliation on a complex weak Fano manifold is algebraically integrable.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/afst.1529
Classification : 37F75

Stéphane Druel 1

1 Institut Fourier, UMR 5582 du CNRS, Université Grenoble Alpes, CS 40700, 38058 Grenoble cedex 9, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
@article{AFST_2017_6_26_1_207_0,
     author = {St\'ephane Druel},
     title = {Regular foliations on weak {Fano} manifolds},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {207--217},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 26},
     number = {1},
     year = {2017},
     doi = {10.5802/afst.1529},
     language = {en},
     url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1529/}
}
TY  - JOUR
AU  - Stéphane Druel
TI  - Regular foliations on weak Fano manifolds
JO  - Annales de la Faculté des sciences de Toulouse : Mathématiques
PY  - 2017
SP  - 207
EP  - 217
VL  - 26
IS  - 1
PB  - Université Paul Sabatier, Toulouse
UR  - https://afst.centre-mersenne.org/articles/10.5802/afst.1529/
DO  - 10.5802/afst.1529
LA  - en
ID  - AFST_2017_6_26_1_207_0
ER  - 
%0 Journal Article
%A Stéphane Druel
%T Regular foliations on weak Fano manifolds
%J Annales de la Faculté des sciences de Toulouse : Mathématiques
%D 2017
%P 207-217
%V 26
%N 1
%I Université Paul Sabatier, Toulouse
%U https://afst.centre-mersenne.org/articles/10.5802/afst.1529/
%R 10.5802/afst.1529
%G en
%F AFST_2017_6_26_1_207_0
Stéphane Druel. Regular foliations on weak Fano manifolds. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 26 (2017) no. 1, pp. 207-217. doi : 10.5802/afst.1529. https://afst.centre-mersenne.org/articles/10.5802/afst.1529/

[1] Michael F. Atiyah Complex analytic connections in fibre bundles, Trans. Am. Math. Soc., Volume 85 (1957), pp. 181-207 | DOI

[2] Paul F. Baum; Raoul Bott On the zeroes of meromorphic vector-fields., Essays on Topology and Related Topics (Mémoires dédiés à Georges de Rham), Springer, 1970, pp. 39-47

[3] Fedor Bogomolov; Michael McQuillan Rational curves on foliated varieties, Foliation theory in algebraic geometry. Proceedings of the conference, New York, NY, USA, September 3–7, 2013, Springer, 2016, pp. 21-51

[4] Jean-Benoît Bost Algebraic leaves of algebraic foliations over number fields, Publ. Math. Inst. Hautes Étud. Sci., Volume 93 (2001), pp. 161-221 | DOI

[5] marco Brunella Feuilletages holomorphes sur les surfaces complexes compactes, Ann. Sci. Éc. Norm. Supér., Volume 30 (1997) no. 5, pp. 569-594

[6] Frédéric Campana; Mihai Păun Foliations with positive slopes and birational stability of orbifold cotangent bundles (http://arxiv.org/abs/1508.02456v1)

[7] Olivier Debarre Higher-dimensional algebraic geometry, Universitext, Springer, 2001, xii+233 pages

[8] Osamu Fujino; Yoshinori Gongyo On images of weak Fano manifolds, Math. Z., Volume 270 (2012) no. 1-2, pp. 531-544 | DOI

[9] Étienne Ghys Feuilletages holomorphes de codimension un sur les espaces homogènes complexes, Ann. Fac. Sci. Toulouse, Volume 5 (1996) no. 3, pp. 493-519 | DOI

[10] Jun-Muk Hwang; Eckart Viehweg Characteristic foliation on a hypersurface of general type in a projective symplectic manifold, Compos. Math., Volume 146 (2010) no. 2, pp. 497-506 | DOI

[11] Stefan Kebekus; Stavros Kousidis; Daniel Lohmann Deformations along subsheaves, Enseign. Math., Volume 56 (2010) no. 3-4, pp. 287-313 | DOI

[12] János Kollár; Shigefumi Mori Birational geometry of algebraic varieties, Cambridge Tracts in Mathematics, 134, Cambridge University Press, 1998, viii+254 pages (Translated from the 1998 Japanese original)

[13] Frederico Lo Bianco; Jorge Vitório Pereira Smooth foliations on homogeneous compact Kähler manifolds, Ann. Fac. Sci. Toulouse, Volume 25 (2016) no. 1, pp. 141-159 | DOI

[14] Victor Loray; Jorge Vitório Pereira; Frédéric Touzet Singular foliations with trivial canonical class (2011) (http://arxiv.org/abs/1107.1538v1)

[15] Yoichi Miyaoka Deformations of a morphism along a foliation and applications, Algebraic geometry, Bowdoin, 1985 (Proc. Sympos. Pure Math.), Volume 46 (1987), pp. 245-268

[16] Shigefumi Mori Projective manifolds with ample tangent bundles, Ann. Math., Volume 110 (1979) no. 3, pp. 593-606 | DOI

[17] Qi Zhang Rational connectedness of log Q-Fano varieties, J. Reine Angew. Math., Volume 590 (2006), pp. 131-142

Cité par Sources :