Mirror Symmetry and Integral Variations of Hodge Structure Underlying One Parameter Families of Calabi-Yau Threefolds

TL;DR

This paper explores the relationship between mirror symmetry and integral variations of Hodge structure in Calabi-Yau threefold families, focusing on classification and geometric realization over the thrice-punctured sphere.

Contribution

It provides a classification of integral variations of Hodge structure for specific Calabi-Yau threefold families and discusses their geometric realization.

Findings

Classification of integral variations of Hodge structure

Analysis of Calabi-Yau threefold families over the thrice-punctured sphere

Insights into geometric realization of Hodge variations

Abstract

This proceedings note introduces aspects of the authors' work relating mirror symmetry and integral variations of Hodge structure. The emphasis is on their classification of the integral variations of Hodge structure which can underly families of Calabi-Yau threefolds over the thrice-punctured sphere with b^3 = 4, or equivalently h^{2,1} = 1, and the related issues of geometric realization of these variations. The presentation parallels that of the first author's talk at the BIRS workshop.