Year: 2026
Type: preprint
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 Kovács--Taji. We exhibit failures of deformation invariance and base change for $1$-Du Bois fibers, showing that the strictness condition is essentially sharp. We also generalize the local-freeness theorem of Friedman--Laza beyond the local complete intersection setting for families over an arbitrary base, and show the unobstructedness of deformations of strict-$1$-Du Bois canonical Calabi-Yau varieties.
Source: arXiv (Cornell University)
Author: Ning, Haoming
Institution: University of Washington
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7202203249