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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
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
Published 30 September 2021