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arXiv · 2601.17894

Rigidity Criterion for Certain Calabi-Yau Families

Ruiran Sun·Chenglong Yu·Kang Zuo
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Abstract

We prove a new rigidity criterion for families of polarized Calabi--Yau manifolds. If, near a boundary point, the total space is smooth, the relative canonical bundle is trivial, and the boundary fiber has only isolated singularities whose summed mixed Hodge spectrum is concentrated, then the family is rigid. This includes degenerations with only ordinary double points and cusps. The proof combines a local vanishing-cycle analysis with a global tensor-product decomposition of the associated variation of Hodge structures. We also prove an infinitesimal version. An explicit non-isotrivial, nonrigid family shows that the isolated-singularity assumption alone is insufficient.

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Ruiran Sun, Chenglong Yu, Kang Zuo. 2026-09-14. Rigidity Criterion for Certain Calabi-Yau Families. https://arxiv.org/abs/2601.17894

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