Singularities of quotient of a vector bundle by a lattice

Question

Let $V$ be a complex vector bundle of rank $g$ over an open unit disc $\Delta$ and $H$ be a integral local system of rank $2g$ over $\Delta$ i.e., for every $t \in \Delta$, $H_t \cong \mathbb{Z}^{2g}$. Suppose that there exists a $\Delta$-morphism $f:H \to V$ which is injective over the punctured unit disc $\Delta^*$, $\ker(f|_{H_0}:H_0 \to V_0) \cong \mathbb{Z}$, for all $t \not= 0$, $f(H_t)$ defines a lattice in $V_t$ and $f(H_0)$ generates $V_0$ as a $\mathbb{C}$-vector space. Then, what kind of singularities does the quotient V/f(H) have? Can the quotient be smooth?