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.
Accepté le :
Publié le :
@article{AFST_2017_6_26_1_207_0,
author = {Druel, St\'ephane},
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 = {http://www.numdam.org/articles/10.5802/afst.1529/}
}
TY - JOUR AU - Druel, Stéphane 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 - http://www.numdam.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 Druel, Stéphane %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 http://www.numdam.org/articles/10.5802/afst.1529/ %R 10.5802/afst.1529 %G en %F AFST_2017_6_26_1_207_0
Druel, Stéphane. 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. http://www.numdam.org/articles/10.5802/afst.1529/
[1] Complex analytic connections in fibre bundles, Trans. Am. Math. Soc., Volume 85 (1957), pp. 181-207 | DOI
[2] 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] 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] Algebraic leaves of algebraic foliations over number fields, Publ. Math. Inst. Hautes Étud. Sci., Volume 93 (2001), pp. 161-221 | DOI
[5] Feuilletages holomorphes sur les surfaces complexes compactes, Ann. Sci. Éc. Norm. Supér., Volume 30 (1997) no. 5, pp. 569-594
[6] Foliations with positive slopes and birational stability of orbifold cotangent bundles (http://arxiv.org/abs/1508.02456v1)
[7] Higher-dimensional algebraic geometry, Universitext, Springer, 2001, xii+233 pages
[8] On images of weak Fano manifolds, Math. Z., Volume 270 (2012) no. 1-2, pp. 531-544 | DOI
[9] Feuilletages holomorphes de codimension un sur les espaces homogènes complexes, Ann. Fac. Sci. Toulouse, Volume 5 (1996) no. 3, pp. 493-519 | DOI
[10] 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] Deformations along subsheaves, Enseign. Math., Volume 56 (2010) no. 3-4, pp. 287-313 | DOI
[12] Birational geometry of algebraic varieties, Cambridge Tracts in Mathematics, 134, Cambridge University Press, 1998, viii+254 pages (Translated from the 1998 Japanese original)
[13] Smooth foliations on homogeneous compact Kähler manifolds, Ann. Fac. Sci. Toulouse, Volume 25 (2016) no. 1, pp. 141-159 | DOI
[14] Singular foliations with trivial canonical class (2011) (http://arxiv.org/abs/1107.1538v1)
[15] Deformations of a morphism along a foliation and applications, Algebraic geometry, Bowdoin, 1985 (Proc. Sympos. Pure Math.), Volume 46, Am. Math. Soc., Providence (1987), pp. 245-268
[16] Projective manifolds with ample tangent bundles, Ann. Math., Volume 110 (1979) no. 3, pp. 593-606 | DOI
[17] Rational connectedness of log -Fano varieties, J. Reine Angew. Math., Volume 590 (2006), pp. 131-142
Cité par Sources :
