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Generic Torelli theorem for one-parameter mirror families to weighted hypersurfaces. (English) Zbl 1185.14006

Summary: One-parameter mirror families to weighted hypersurfaces are already constructed and well studied. A generic Torelli theorem for quintic-mirror family is proved by S. Usui [Proc. Japan Acad., Ser. A 84, No. 8, 143–146 (2008; Zbl 1164.14003)]. In this article, we give the proof of a generic Torelli theorem for the other families after Usui’s proof for quintic-mirror family.

MSC:

14C34 Torelli problem
14D07 Variation of Hodge structures (algebro-geometric aspects)
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
32G20 Period matrices, variation of Hodge structure; degenerations

Citations:

Zbl 1164.14003
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References:

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