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On Levi-flat hypersurfaces tangent to holomorphic webs
Arturo Fernández-Pérez1
1 Departamento de Matemática, UFMG, Av. Antônio Carlos, 6627 C.P. 702, 30123-970 – Belo Horizonte – MG, Brazil.
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 20 (2011) no. 3, pp. 581-597.

We investigate real analytic Levi-flat hypersurfaces tangent to holomorphic webs. We introduce the notion of first integrals for local webs. In particular, we prove that a k-web with finitely many invariant subvarieties through the origin tangent to a Levi-flat hypersurface has a holomorphic first integral.

Nous étudions les hypersurfaces analytiques réelles Levi-plates tangentes à un tissu holomorphe. Nous introduisons la notion d’intégrale première pour un tissu défini localement. En particulier, nous prouvons qu’un k-tissu admettant un nombre fini de sous-variétés invariantes passant par l’origine et tangentes à une hypersurface Levi-plate possède une intégrale première holomorphe.

DOI: 10.5802/afst.1318

Arturo Fernández-Pérez 1

1 Departamento de Matemática, UFMG, Av. Antônio Carlos, 6627 C.P. 702, 30123-970 – Belo Horizonte – MG, Brazil. 
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     title = {On {Levi-flat} hypersurfaces tangent to holomorphic webs},
     journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
     pages = {581--597},
     publisher = {Universit\'e Paul Sabatier, Institut de Math\'ematiques},
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     volume = {Ser. 6, 20},
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Arturo Fernández-Pérez. On Levi-flat hypersurfaces tangent to holomorphic webs. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 20 (2011) no. 3, pp. 581-597. doi : 10.5802/afst.1318. https://afst.centre-mersenne.org/articles/10.5802/afst.1318/

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