Analyse fonctionnelle
Transversely product singularities of foliations in projective spaces
Comptes Rendus. Mathématique, Tome 361 (2023) no. G11, pp. 1785-1787

We prove that a transversely product component of the singular set of a holomorphic foliation on n is necessarily a Kupka component.

Reçu le :
Révisé le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.528

Rosas, Rudy 1

1 Departamento de Ciencias, Pontificia Universidad Católica del Perú, Av. Universitaria 1801, Lima, Perú
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
@article{CRMATH_2023__361_G11_1785_0,
     author = {Rosas, Rudy},
     title = {Transversely product singularities of foliations in projective spaces},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1785--1787},
     year = {2023},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {361},
     number = {G11},
     doi = {10.5802/crmath.528},
     language = {en},
     url = {https://www.numdam.org/articles/10.5802/crmath.528/}
}
TY  - JOUR
AU  - Rosas, Rudy
TI  - Transversely product singularities of foliations in projective spaces
JO  - Comptes Rendus. Mathématique
PY  - 2023
SP  - 1785
EP  - 1787
VL  - 361
IS  - G11
PB  - Académie des sciences, Paris
UR  - https://www.numdam.org/articles/10.5802/crmath.528/
DO  - 10.5802/crmath.528
LA  - en
ID  - CRMATH_2023__361_G11_1785_0
ER  - 
%0 Journal Article
%A Rosas, Rudy
%T Transversely product singularities of foliations in projective spaces
%J Comptes Rendus. Mathématique
%D 2023
%P 1785-1787
%V 361
%N G11
%I Académie des sciences, Paris
%U https://www.numdam.org/articles/10.5802/crmath.528/
%R 10.5802/crmath.528
%G en
%F CRMATH_2023__361_G11_1785_0
Rosas, Rudy. Transversely product singularities of foliations in projective spaces. Comptes Rendus. Mathématique, Tome 361 (2023) no. G11, pp. 1785-1787. doi: 10.5802/crmath.528

[1] Brunella, Marco Sur les feuilletages de l’espace projective ayant une composante de Kupka, Enseign. Math., Volume 55 (2009) no. 3-4, pp. 227-234 | DOI | Zbl

[2] Calvo-Andrade, Omegar Foliations with a Kupka component on Algebraic Manifolds, Bol. Soc. Bras. Mat., Volume 30 (1999) no. 2, pp. 183-197 | DOI | MR | Zbl

[3] Calvo-Andrade, Omegar Foliations of codimension greater than one with a Kupka component, Qual. Theory Dyn. Syst., Volume 8 (2009) no. 2, pp. 241-253 | Zbl | DOI | MR

[4] Calvo-Andrade, Omegar Foliations with a radial Kupka set on projective spaces, Bull. Braz. Math. Soc. (N.S.), Volume 47 (2016) no. 4, pp. 1071-1083 | DOI | MR | Zbl

[5] Calvo-Andrade, Omegar; Corrêa, Mauricio; Fernández-Pérez, Arturo Higher codimensional foliations with Kupka singularities, Int. J. Math., Volume 28 (2017) no. 3, 1750019, 29 pages | MR | Zbl

[6] Cerveau, Dominique; Lins-Neto, Alcides Codimension-one foliations in P n , n3, with Kupka components, Complex analytic methods in dynamical systems (Astérisque), Volume 222, Société Mathématique de France, 1994, pp. 93-132 | Zbl

[7] Kupka, Ivan The singularities of integrable structurally stable pfaffian forms, Proc. Natl. Acad. Sci. USA, Volume 52 (1964), pp. 1431-1432 | DOI | MR | Zbl

[8] Lins-Neto, Alcides Local transversely product singularities, Ann. Henri Lebesgue, Volume 4 (2021), pp. 485-502 | DOI | MR | Numdam | Zbl

[9] de Medeiros, Airton S. Structural stability of integrable differential forms, Geometry and Topology (Lecture Notes in Mathematics), Springer, 1977, pp. 395-428 | DOI | MR | Zbl

Cité par Sources :