Isotropic transformations of germs of holomorphic foliations (Q1305125)

This paper deals with the germs of holomorphic diffeomorphisms \(\text{Diff}(\mathbb{C}^{n},0)\) preserving a germ of holomorphic foliation at the origin of \(\mathbb{C}^{n}\). Let \(\mathfrak F_{\omega}\) be a germ of holomorphic singular foliation at the origin of \(\mathbb{C}^{n}\) defined by the equation \(\omega =0\), where \(\omega\) is a germ of holomorphic integrable 1-form, i. e., satisfying \(\omega \wedge d\omega = 0\). The main result is about the description of the (sub)group of isotropic transformations of \(\mathfrak F_{\omega}\), which is defined as follows: \[ \text{Iso}({\mathfrak F}_{\omega}) = \{\phi \in \text{Diff}(\mathbb{C}^{n},0), \phi^{*} \omega \wedge \omega = 0\}. \]