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Stability of foliations induced by rational maps
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Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 18 (2009) no. 4, p. 685-715

We show that the singular holomorphic foliations induced by dominant quasi-homogeneous rational maps fill out irreducible components of the space q (r,d) of singular foliations of codimension q and degree d on the complex projective space r , when 1qr-2. 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 q (r,d) des feuilletages de codimension q et degré d de l’espace projectif r pour tout 1qr-2. Nous étudions la géométrie de telles composantes irréductibles. Nous montrons que ce sont des variétés rationnelles et calculons leur degré dans plusieurs cas.

Received : 2008-02-22
Accepted : 2008-06-27
Published online : 2010-01-04
DOI : https://doi.org/10.5802/afst.1221
@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},
     publisher = {Universit\'e Paul Sabatier, Toulouse},
     volume = {Ser. 6, 18},
     number = {4},
     year = {2009},
     pages = {685-715},
     doi = {10.5802/afst.1221},
     mrnumber = {2590385},
     zbl = {1208.32029},
     language = {en},
     url={afst.centre-mersenne.org/item/AFST_2009_6_18_4_685_0/}
}
Cukierman, F.; Pereira, J. V.; Vainsencher, I. 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/item/AFST_2009_6_18_4_685_0/

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