  We prove non-degeneracy of the cohomological bulk and boundary traces for
general open-closed Landau-Ginzburg models associated to a pair $(X,W)$, where
$X$ is a non-compact complex manifold with trivial canonical line bundle and
$W$ is a complex-valued holomorphic function defined on $X$, assuming only that
the critical locus of $W$ is compact (but may not consist of isolated points).
These results can be viewed as certain "deformed" versions of Serre duality.
The first amounts to a duality property for the hypercohomology of the sheaf
Koszul complex of $W$, while the second is equivalent with the statement that a
certain power of the shift functor is a Serre functor on the even subcategory
of the $\mathbb{Z}_2$-graded category of topological D-branes of such models.
