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Let $\Omega \subset \mathbb{C}^m$ be an open, connected and bounded set and$\mathcal{A}(\Omega)$ be a function algebra of holomorphic functions on$\Omega$. In this article we study quotient Hilbert modules obtained fromsubmodules, consisting of functions in $\mathcal{M}$ vanishing to order $k$along a smooth irreducible complex analytic set $\mathcal{Z}\subset\Omega$ ofcodimension at least $2$, of a quasi-free Hilbert module, $\mathcal{M}$. Ourmotive is to investigate unitary invariants of such quotient modules. Wecompletely determine unitary equivalence of aforementioned quotient modules andrelate it to geometric invariants of a Hermitian holomorphic vector bundles.Then, as an application, we characterize unitary equivalence classes ofweighted Bergman modules over $\mathcal{A}(\mathbb{D}^m)$ in terms of those ofquotient modules arising from the submodules of functions vanishing to order$2$ along the diagonal in $\mathbb{D}^m$.

On unitary invariants of quotient Hilbert modules along smooth complex analytic sets