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This is a Quantitative Study study.

October 10, 2025Open Access

Fibering out Calabi-Yau motives

Key Points

Proving the modularity of mixed periods reveals deeper insights into algebraic geometry.
Period computations include classical and new periods related to meromorphic modular forms, enhancing existing theories.
The methodology involves expressing periods as integrals of families of K3 surfaces, bridging these distinct mathematical domains.
The research uncovers novel periods tied to non-vanishing residues, indicating potential pathways for further exploration.

Abstract

We prove the modularity of mixed periods associated with singular fibers of specific families of Calabi-Yau threefolds. This is done by "fibering out", i.e. by expressing these periods as integrals of periods of families of K3 surfaces and by using modularity properties of the latter. Besides classical periods of holomorphic modular forms and meromorphic modular forms with vanishing residues, the computations lead to new interesting periods associated with meromorphic modular forms with non-vanishing residues as well as contours between CM points.

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Cite This Study

Bönisch et al. (Sat,) studied this question.

synapsesocial.com/papers/68e8ed7aa1d181ff1b94810f https://doi.org/https://doi.org/10.48550/arxiv.2510.03939

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