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

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}.