Frobenius theorem for foliations on singular varieties (Q734071)

In this paper, the authors present a generalization of Malgrange's Frobenius Singular Theorem to certain germs of analytic foliations of germs of irreducible analytic subsets \(X\) of \(\mathbb{C}^N\). A particular case of interest is where \(X\) is a complete intersection and \(\mathrm{dim}(\mathrm{sing}(X))\leq \mathrm{dim}(X)-3\). The proof uses in particular a construction by Godbillon of a \textit{Godbillon-Vey sequence} associated to an integrable \(1\)-form \(\omega\) satisfying \(\mathrm{cod}(\mathrm{sing}(\omega))\geq 3\).