Local Mirror Symmetry and Type IIA Monodromy of Calabi-Yau manifolds

TL;DR

This paper introduces a monodromy invariant pairing for mirror Calabi-Yau pairs, interprets hypergeometric series via homological mirror symmetry, and explores local mirror symmetry limits to del Pezzo surfaces.

Contribution

It explicitly identifies a monodromy invariant pairing and connects hypergeometric series with homological mirror symmetry in the context of Calabi-Yau manifolds.

Findings

Explicit monodromy invariant pairing for mirror Calabi-Yau manifolds.

Interpretation of hypergeometric series through homological mirror symmetry.

Analysis of local mirror symmetry limits to del Pezzo surfaces.

Abstract

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.