2018/06/13 by Fernández-Pérez, Arturo, Támara, Jimmy
#32S65 #32V40 #Complex Variables (math.CV) #Dynamical Systems (math.DS) #FOS: Mathematics
paper · doi:10.48550/arxiv.1806.04958
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.