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arXiv · 1806.04958

Lehmann-Suwa residues of codimension one holomorphic foliations and applications

Arturo Fernández-Pérez·Jimmy Támara
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Abstract

Let $\mathcal{F}$ be a singular codimension one holomorphic foliation on a compact complex manifold $X$ of dimension at least three such that its singular set has codimension at least two. In this paper, we determine Lehmann-Suwa residues of $\mathcal{F}$ as multiples of complex numbers by integration currents along irreducible complex subvarieties of $X$. We then prove a formula that determines the Baum-Bott residue of simple almost Liouvillian foliations of codimension one, in terms of Lehmann-Suwa residues, generalizing a result of Marco Brunella. As an application, we give sufficient conditions for the existence of dicritical singularities of a singular real-analytic Levi-flat hypersurface $M\subset X$ tangent to $\mathcal{F}$.

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Arturo Fernández-Pérez, Jimmy Támara. 2018-06-13. Lehmann-Suwa residues of codimension one holomorphic foliations and applications. https://arxiv.org/abs/1806.04958

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