Type II/F-theory Superpotentials and Ooguri-Vafa Invariants of Compact   Calabi-Yau Threefolds with Three Deformations
  We calculate the D-brane superpotentials for two Calabi-Yau manifolds with three deformations by the generalized hypergeometric GKZ systems, which give rise to the flux superpotentials $\mathcal{W}_{GVW}$ of the dual F-theory compactification on the relevant Calabi-Yau fourfolds in the weak decoupling limit. We also compute the Ooguri-Vafa invariants from A-model expansion with mirror symmetry, which are related to the open Gromov-Witten invariants. 
Feng-Jun Xu, Fu-Zhong Yang
hep-th math-ph math.AG math.MP