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

Lehmann-Suwa residues of codimension one holomorphic foliations and applications