# Poincare duality in families of smooth, projective curves

Let $$f:\mathcal{C} \to \Delta^*$$ be a family of smooth, projective curves over a punctured disc. Denote by $$\mathbb{H}^1:=R^1f_*\mathbb{Z}$$ the associated local system, such that for every $$t \in \Delta^*$$, the fiber $$\mathbb{H}^1_t \cong H^1(\mathcal{C}_t,\mathbb{Z})$$. My question is: Is there a Poincare duality associated to the local system? In particular, does there exist an isomorphism of sheaves: $$\mathbb{H}^1 \to \mathcal{H}om(\mathbb{H}^1, \mathbb{Z}_{\Delta^*}),$$ where $$\mathcal{H}om$$ denotes sheaf homomorphism and $$\mathbb{Z}_{\Delta^*}$$ is the constant sheaf on $$\Delta^*$$ with stalk $$\mathbb{Z}$$. Any reference will be most welcome.