Germs of singular Levi-flat hypersurfaces and holomorphic foliations

TL;DR

This paper demonstrates that the Levi foliation of a real analytic Levi-flat hypersurface can be extended to a $d$-web near nondicritical singular points and admits a multiple-valued meromorphic first integral, revealing new structural insights.

Contribution

It introduces a method to extend Levi foliations to $d$-webs and shows the existence of a multiple-valued meromorphic first integral near singularities.

Findings

Levi foliation extends to a $d$-web near nondicritical singular points.

Existence of a multiple-valued meromorphic first integral.

Provides structural understanding of Levi-flat hypersurfaces near singularities.

Abstract

It is shown that the Levi foliation of a real analytic Levi-flat hypersurface extends to a $d$-web near a nondicritical singular point and admits a multiple-valued meromorphic first integral.