Asian Journal of Mathematics

Volume 25 (2021)

Number 1

Degenerating Hodge structure of one–parameter family of Calabi–Yau threefolds

Pages: 31 – 42

DOI: https://dx.doi.org/10.4310/AJM.2021.v25.n1.a2

Authors

Tatsuki Hayama (School of Business Administration, Senshu University, Kawasaki, Kanagawa, Japan)

Atsushi Kanazawa (Department of Mathematics, Kyoto University, Sakyo, Kyoto, Japan)

Abstract

To a one-parameter family of Calabi–Yau threefolds, we can associate the extended period map by the $\operatorname{log}$ Hodge theory of Kato and Usui. We study the image of a maximally unipotent monodromy point under the extended period map. As an application, we prove the generic Torelli theorem for a large class of one-parameter families of Calabi–Yau threefolds.

Keywords

($\operatorname{log}$) Hodge theory, Calabi–Yau, Torelli problem, mirror symmetry

2010 Mathematics Subject Classification

14C30, 14C34, 14J32

Received 11 September 2015

Accepted 13 March 2020