Local Mirror Symmetry and Type IIA Monodromy of Calabi-Yau manifolds
  We propose a monodromy invariant pairing $K_{hol}(X) \otimes H_3(X^\vee,\ZZ) \to \IQ$ for a mirror pair of Calabi-Yau manifolds, $(X,X^\vee)$. This pairing is utilized implicitly in the previous calculations of the prepotentials for Gromov-Witten invariants. After identifying the pairing explicitly we interpret some hypergeometric series from the viewpoint of homological mirror symmetry due to Kontsevich. Also we consider the local mirror symmetry limit to del Pezzo surfaces in Calabi-Yau 3-folds. 
S. Hosono