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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 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.

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Cite

BibTeXRIS
BibTeX
@misc{ning2026deformations,
  title = {{Deformations, local freeness, and base change for higher Du Bois singularities}},
  author = {Haoming Ning},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2608.07849},
  eprint = {2608.07849},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.07849},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Deformations, local freeness, and base change for higher Du Bois singularities
AU  - Haoming Ning
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2608.07849
UR  - https://arxiv.org/abs/2608.07849
AB  - 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.
ER  -