On Levi-flat hypersurfaces tangent to holomorphic webs

Details On Levi-flat hypersurfaces tangent to holomorphic webs On Levi-flat hypersurfaces tangent to holomorphic webs

2011-09-08

arxiv.org/abs/1109.1608v2

Mathematics

Complex Variables

Accepted for publication in Ann. Fac. Sci. Toulouse

Scientific paper

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

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