Vietnam Journal of Mathematics

, Volume 42, Issue 3, pp 345–363 | Cite as

Log Hodge Theoretic Formulation of Mirror Symmetry for Calabi–Yau Threefolds

  • Sampei UsuiEmail author


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.


Log Hodge theory Mirror symmetry Calabi–Yau threefold 

Mathematics Subject Classification (2010)

Primary 14C30 Secondary 14D07 32G20 



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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Copyright information

© Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2014

Authors and Affiliations

  1. 1.Graduate School of ScienceOsaka UniversityToyonakaJapan

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