[Géométrie birationnelle des feuilletages associés à des dérivations simples]
We propose a study of the foliations of the projective plane induced by simple derivations of the polynomial ring in two indeterminates over the complex field. These correspond to foliations which have no invariant algebraic curve nor singularities in the complement of a line. We establish the position of these foliations in the birational classification of foliations and prove the finiteness of their birational symmetries. Most of the results apply to wider classes of foliations.
Nous proposons une étude des feuilletages du plan projectif qui sont induits par une dérivation simple de l’anneau des polynômes à deux indéterminées sur le corps des complexes. Il s’agit des feuilletages qui ne possèdent ni courbe algébrique ni singularité dans le complémentaire d’une droite. Nous donnons leur emplacement dans la classification birationnelle des feuilletages et prouvons la finitude de leurs groupes de symétries birationnelles. La plupart des résultats s’applique en fait à des classes plus larges de feuilletages.
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DOI : 10.24033/bsmf.2793
Keywords: Holomorphic foliations, Birational geometry, Derivations
Mots-clés : Feuilletages holomorphes, Géométrie birationnelle, Dérivations
Cousin, Gaël 1 ; Mendes, Luís Gustavo 2 ; Pan, Iván 3
@article{BSMF_2019__147_4_607_0,
author = {Cousin, Ga\"el and Mendes, Lu{\'\i}s Gustavo and Pan, Iv\'an},
title = {Birational geometry of foliations associated to simple derivations},
journal = {Bulletin de la Soci\'et\'e Math\'ematique de France},
pages = {607--638},
year = {2019},
publisher = {Soci\'et\'e math\'ematique de France},
volume = {147},
number = {4},
doi = {10.24033/bsmf.2793},
mrnumber = {4057712},
zbl = {1446.14006},
language = {en},
url = {https://www.numdam.org/articles/10.24033/bsmf.2793/}
}
TY - JOUR AU - Cousin, Gaël AU - Mendes, Luís Gustavo AU - Pan, Iván TI - Birational geometry of foliations associated to simple derivations JO - Bulletin de la Société Mathématique de France PY - 2019 SP - 607 EP - 638 VL - 147 IS - 4 PB - Société mathématique de France UR - https://www.numdam.org/articles/10.24033/bsmf.2793/ DO - 10.24033/bsmf.2793 LA - en ID - BSMF_2019__147_4_607_0 ER -
%0 Journal Article %A Cousin, Gaël %A Mendes, Luís Gustavo %A Pan, Iván %T Birational geometry of foliations associated to simple derivations %J Bulletin de la Société Mathématique de France %D 2019 %P 607-638 %V 147 %N 4 %I Société mathématique de France %U https://www.numdam.org/articles/10.24033/bsmf.2793/ %R 10.24033/bsmf.2793 %G en %F BSMF_2019__147_4_607_0
Cousin, Gaël; Mendes, Luís Gustavo; Pan, Iván. Birational geometry of foliations associated to simple derivations. Bulletin de la Société Mathématique de France, Tome 147 (2019) no. 4, pp. 607-638. doi: 10.24033/bsmf.2793
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