Let $\mathscr{F}$ 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 $\mathscr{F}$ 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 $\mathscr{F}$.

中文翻译：

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余维一全同叶的Lehmann–Suwa残基及其应用

令$ \ mathscr {F} $为奇异余维，其紧实复流形$ X $的维上至少为3，使得其奇异集的余维至少为2。在本文中，我们通过沿$ X $的不可约复杂子变量的积分电流，确定$ \ mathscr {F} $的Lehmann–Suwa残基为复数的倍数。然后，我们证明了一个公式，该公式可以根据Lehmann-Suwa残差来确定余量维一的简单几乎Liouvillian叶面的Baum-Bott残差，并推广了Marco Brunella的结果。作为一个应用，我们为奇异的实际解析李维平超曲面$ M \ subset X $与$ \ mathscr {F} $的切线的双临界奇点的存在提供了充分的条件。