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Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



Periods of tropical Calabi–Yau hypersurfaces

Author: Yuto Yamamoto
Journal: J. Algebraic Geom. 31 (2022), 303-343
Published electronically: December 20, 2021
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Abstract | References | Additional Information

Abstract: We consider the residual B-model variation of Hodge structure of Iritani defined by a family of toric Calabi–Yau hypersurfaces over a punctured disk $D \setminus \left \{ 0\right \}$. It is naturally extended to a logarithmic variation of polarized Hodge structure of Kato–Usui on the whole disk $D$. By restricting it to the origin, we obtain a polarized logarithmic Hodge structure (PLH) on the standard log point. In this paper, we describe the PLH in terms of the integral affine structure of the dual intersection complex of the toric degeneration in the Gross–Siebert program.

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Additional Information

Yuto Yamamoto
Affiliation: Center for Geometry and Physics, Institute for Basic Science (IBS), Pohang 37673, Republic of Korea
MR Author ID: 1166484

Received by editor(s): February 11, 2020
Received by editor(s) in revised form: August 3, 2020, September 10, 2020, and September 14, 2020
Published electronically: December 20, 2021
Additional Notes: This work was supported by IBS-R003-D1, Grant-in-Aid for JSPS Research Fellow (18J11281), and the Program for Leading Graduate Schools, MEXT, Japan. The author was financially supported by Sam Payne for the visit to Yale University. The visit to University of Cambridge was supported by JSPS Overseas Challenge Program for Young Researchers.
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