arXiv subjects

Haoming Ning

Publications and source records attributed to Haoming Ning.

3 recordsLinked to original sources

arXiv2026

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

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.

math.AG↗

arXiv2025

Higher Du Bois and Higher Rational Pairs

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, including Bertini type theorems, stability under finite maps and that m-rational pairs are m-Du Bois. We prove these using a generalized Kov\'acs-Schwede-type injectivity theorem for pairs, the main technical result of this paper.

math.AG↗

arXiv2022

Symplectic embeddings of four-dimensional polydisks into half integer ellipsoids

We obtain new sharp obstructions to symplectic embeddings of four-dimensional polydisks $P(a,1)$ into four-dimensional ellipsoids $E(bc,c)$ when $1\le a< 2$ and $b$ is a half-integer. When $1 \leq a < 2-O(b^{-1})$ we demonstrate that $P(a,1)$ symplectically embeds into $E(bc,c)$ if and only if $a+b\le bc$. Our results show that inclusion is optimal and extend the result by Hutchings \cite{H} when $b$ is an integer. Our proof is based on a combinatorial criterion developed by Hutchings \cite{H} to obstruct symplectic embeddings.

math.SG↗