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arXiv · 2608.07849

Deformations, local freeness, and base change for higher Du Bois singularities

Haoming Ning
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Abstract

We prove that strict higher Du Bois singularities are invariant under small deformations. Using this, we prove a base change theorem for the relative Du Bois complex with strict higher Du Bois fibers, answering a question of Kov\'acs--Taji. We exhibit failures of deformation invariance and base change for $1$-Du Bois fibers, showing that the strictness condition is essentially sharp. As applications of base change, we generalize the local-freeness theorem of Friedman--Laza beyond the local complete intersection setting for families over a smooth curve, and prove constancy of Hodge numbers for families over an arbitrary base.

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Haoming Ning. 2026-08-08. Deformations, local freeness, and base change for higher Du Bois singularities. https://arxiv.org/abs/2608.07849

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