Given a holomorphic singular foliation ${\mathcal {F}}$ of $({\mathbb {C}}^n,0)$, we define $\textrm {Iso}({\mathcal {F}})$ as the group of germs of biholomorphisms on $({\mathbb {C}}^n,0)$ preserving ${\mathcal {F}}$: $\textrm {Iso}({\mathcal {F}})\!=\!\lbrace \Phi \in \textrm {Diff}({\mathbb {C}}^n,0)\,|\,\Phi ^*({\mathcal {F}})\!=\!{\mathcal {F}}\rbrace $. The normal subgroup of $\textrm {Iso}({\mathcal {F}})$, of biholomorphisms sending each leaf of ${\mathcal {F}}$ into itself, will be denoted as $\textrm {Fix}({\mathcal {F}})$. The corresponding groups of formal biholomorphisms will be denoted as $\widehat {\textrm {Iso}}({\mathcal {F}})$ and $\widehat {\textrm {Fix}}({\mathcal {F}})$, respectively. The purpose of this paper will be to study the quotients $\textrm {Iso}({\mathcal {F}})/\textrm {Fix}({\mathcal {F}})$ and $\widehat {\textrm {Iso}}({\mathcal {F}})/\widehat {\textrm {Fix}}({\mathcal {F}})$, mainly in the case of codimension one foliation.

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叶的各向同性群：局部案例

给定一个 $({\mathbb {C}}^n,0)$ 的全纯奇异叶化 ${\mathcal {F}}$，我们将 $\textrm {Iso}({\mathcal {F}})$ 定义为$({\mathbb {C}}^n,0)$ 上的双全同胚群保留 ${\mathcal {F}}$: $\textrm {Iso}({\mathcal {F}})\! =\!\lbrace \Phi \in \textrm {Diff}({\mathbb {C}}^n,0)\,|\,\Phi ^*({\mathcal {F}})\!=\! {\mathcal {F}}\rbrace $. $\textrm {Iso}({\mathcal {F}})$ 的正规子群，将 ${\mathcal {F}}$ 的每个叶发送到自身的双全同态，将表示为 $\textrm {Fix}( {\mathcal {F}})$。相应的形式双全同态组将表示为 $\widehat {\textrm {Iso}}({\mathcal {F}})$ 和 $\widehat {\textrm {Fix}}({\mathcal {F}}) $，分别。