Hodge rigidity of Chern classes
Algebraic Geometry
2026-03-27 v1
Abstract
In this paper, we study the homogeneous components of the Chern--Schwartz--MacPherson (CSM) classes of Schubert cells. We prove that, under suitable conditions, each such component is represented by an irreducible subvariety. In particular, our result extends Huh's result \cite{Huh} by relaxing the regularity assumption on log resolutions. As a consequence, the conclusion holds for all cominuscule Schubert cells of classical type and for a large family of exceptional cases. We also obtain analogous results for certain Schubert varieties in symplectic Grassmannians and flag varieties.
Keywords
Cite
@article{arxiv.2603.25456,
title = {Hodge rigidity of Chern classes},
author = {Yuxiang Liu and Artan Sheshmani and Shing-Tung Yau},
journal= {arXiv preprint arXiv:2603.25456},
year = {2026}
}