Studies of closed/open mirror symmetry for quintic threefold through log mixed Hodge theory

TL;DR

This paper refines the understanding of mirror symmetry for quintic threefolds by applying log mixed Hodge theory and integral structures, providing new insights into open mirror symmetry and Neron models.

Contribution

It introduces a precise integral structure for studying open mirror symmetry of quintic threefolds using log mixed Hodge theory, building on Iritani's framework.

Findings

Clarified the integral structures in mirror symmetry contexts.

Applied log mixed Hodge theory to open mirror symmetry.

Connected asymptotic conditions with Neron models.

Abstract

We correct the definitions and descriptions of the integral structures in [U14]. The previous flat basis in [ibid] is characterized by the Frobenius solutions and integral in the first approximation by mean of the graded quotients of monodromy filtration, but not integral in the strict sense. In this article, we use the integral structure of Iritani in [I11] for A-model. Using this precise version, we study open mirror symmetry for quintic threefolds through log mixed Hodge theory, especially the recent result on Neron models for admissible normal functions with non-torsion extensions in the joint work [KNU14] with K. Kato and C. Nakayama. We understand asymptotic conditions as values in the fiber over a base point on the boundary of S^{log}.