  Compactifications with fluxes and branes motivate us to study various
enumerative invariants of Calabi-Yau manifolds. In this paper, we study
non-perturbative corrections depending on both open and closed string moduli
for a class of compact Calabi-Yau manifolds in general dimensions. Our analysis
is based on the methods using relative cohomology and generalized
hypergeometric system. For the simplest example of compact Calabi-Yau fivefold,
we explicitly derive the associated Picard-Fuchs differential equations and
compute the quantum corrections in terms of the open and closed flat
coordinates. Implications for a kind of open-closed duality are also discussed.

High Energy Physics - Theory;Algebraic Geometry