Stability of closed leaves holomorphic foliations via torsion behavior of groups of germs

Consider a compact leaf $\mathcal{L}$ of a holomorphic foliation $\mathcal{F}$ such that all the leaves of the restriction of $\mathcal{F}$ to some neighborhood $U$ of $\mathcal{L}$ are closed in $U$. We show that there exists an invariant germ of analytic set $V$ in a neighborhood of $\mathcal{L}$,