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math.AG2026
Relative Du Bois complexes over higher dimensional bases
Dora Kassabova, Haoming Ning
We extend the notion of the right relative Du Bois complex to a smooth base of arbitrary dimension. We further show that this complex satisfies base change in the sense of Kovács--…
math.AG2026
Deformations, local freeness, and base change for higher Du Bois singularities
Haoming Ning
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 hi…
math.AG2025
Higher Du Bois and Higher Rational Pairs
Haoming Ning, Brian Nugent
We extend the notions of higher Du Bois and higher rational singularities to pairs in the sense of the minimal model program. We extend numerous results to these higher pairs, incl…