The variety of moduli of foliations on a complex space (Q1099300)

Let X be a complex space and \(\Omega\) be the sheaf of holomorphic l-forms on X. Let \(\Omega\) ' be a coherent subsheaf of \(\Omega\) and X' be an irreducible component of X. \(\Omega\) ' is called a X'-foliation if there is a thin analytic subset A of X' containing the singular locus of X in X' such that \(\Omega '/X'\setminus A\) defines a regular foliation. Let Y, Z be other complex spaces. Let Ř be a coherent analytic subsheaf of \(\Omega^ Y\) such that \(R:=\Omega^ Y/\check R\) is Y-flat. The author proves that the set \(F_{X'}(Y,\check R)\) of all points y of Y such that Ř(y) is a X'-foliation is an analytic subset of Y.