Some Properties of Hypergeometric Series Associated with Mirror Symmetry

TL;DR

This paper investigates properties of hypergeometric series linked to mirror symmetry in Calabi-Yau hypersurfaces, aiding in the computation of genus one Gromov-Witten invariants in algebraic geometry and string theory.

Contribution

It identifies key properties of hypergeometric series that facilitate the verification of BCOV predictions and the calculation of Gromov-Witten invariants.

Findings

Hypergeometric series satisfy specific mathematical properties.

These properties are used to verify BCOV predictions.

They enable computation of genus one Gromov-Witten invariants.

Abstract

We show that certain hypergeometric series used to formulate mirror symmetry for Calabi-Yau hypersurfaces, in string theory and algebraic geometry, satisfy a number of interesting properties. Many of these properties are used in separate papers to verify the BCOV prediction for the genus one Gromov-Witten invariants of a quintic threefold and more generally to compute the genus one Gromov-Witten invariants of any Calabi-Yau projective hypersurface.