Lehmann-Suwa Residues Of Codimension One Holomorphic Foliations And Applications

Fern´Andez-P´Erez A.; T´Amara J. · Asian Journal of Mathematics (2020) · DOI: 10.4310/ajm.2020.v24.n4.a6

Resumen

Let 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 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 ⊂ X tangent to F.