Abstract
We hope to understand the Hodge theoretic aspect of mirror symmetry in the framework of the fundamental diagram of log mixed Hodge theory. We give a formulation of mirror conjecture for Calabi–Yau threefolds as the coincidence of log period maps with specified sections under the mirror map. Since a variation of Hodge structure with unipotent monodromies on a product of punctured discs uniquely extends over the puncture to a log Hodge structure, we can work on the boundary point over which the log Riemann–Hilbert correspondence exists, and we can observe clearly in high resolution the behavior of Z-structure over the boundary point (cf. notes in Introduction below). This is an advantage of log Hodge theory.
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Acknowledgments
The author would like to thank Kazuya Kato and Chikara Nakayama for the exciting collaborations and useful comments. The author would like to thank the referees for the important information and helpful comments. The author would like to thank Hiroshi Iritani who pointed out that the treatment of Z-structure in Sections 3.4 and 3.5 in the old version was insufficient.
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Dedicated to Professor Hideyasu Sumihiro
Partially supported by JSPS KAKENHI (B) No. 23340008.
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Usui, S. Log Hodge Theoretic Formulation of Mirror Symmetry for Calabi–Yau Threefolds. Vietnam J. Math. 42, 345–363 (2014). https://doi.org/10.1007/s10013-014-0085-z
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DOI: https://doi.org/10.1007/s10013-014-0085-z