We show that the singular holomorphic foliations induced by dominant quasi-homogeneous rational maps fill out irreducible components of the space of singular foliations of codimension and degree on the complex projective space , when . We study the geometry of these irreducible components. In particular we prove that they are all rational varieties and we compute their projective degrees in several cases.
Nous montrons que les feuilletages holomorphes induits par les applications rationnelles quasi-homogènes remplissent les composantes irréductibles de l’espace des feuilletages de codimension et degré de l’espace projectif pour tout . Nous étudions la géométrie de telles composantes irréductibles. Nous montrons que ce sont des variétés rationnelles et calculons leur degré dans plusieurs cas.
@article{AFST_2009_6_18_4_685_0,
author = {F. Cukierman and J. V. Pereira and I. Vainsencher},
title = {Stability of foliations induced by rational maps},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {685--715},
publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
address = {Toulouse},
volume = {Ser. 6, 18},
number = {4},
year = {2009},
doi = {10.5802/afst.1221},
mrnumber = {2590385},
zbl = {1208.32029},
language = {en},
url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1221/}
}
TY - JOUR AU - F. Cukierman AU - J. V. Pereira AU - I. Vainsencher TI - Stability of foliations induced by rational maps JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2009 SP - 685 EP - 715 VL - 18 IS - 4 PB - Université Paul Sabatier, Institut de Mathématiques PP - Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1221/ DO - 10.5802/afst.1221 LA - en ID - AFST_2009_6_18_4_685_0 ER -
%0 Journal Article %A F. Cukierman %A J. V. Pereira %A I. Vainsencher %T Stability of foliations induced by rational maps %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2009 %P 685-715 %V 18 %N 4 %I Université Paul Sabatier, Institut de Mathématiques %C Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1221/ %R 10.5802/afst.1221 %G en %F AFST_2009_6_18_4_685_0
F. Cukierman; J. V. Pereira; I. Vainsencher. Stability of foliations induced by rational maps. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 18 (2009) no. 4, pp. 685-715. doi : 10.5802/afst.1221. https://afst.centre-mersenne.org/articles/10.5802/afst.1221/
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