The arithmetic rank of determinantal nullcones
Commutative Algebra
2026-02-18 v2 Algebraic Geometry
Representation Theory
Abstract
We compute the arithmetic rank as well as the local/\'etale cohomological dimension of nullcone ideals arising from the classical actions of the symplectic group, the general linear group, and the orthogonal group. We use these calculations to establish striking vanishing results for local cohomology modules supported at these nullcone ideals; this is achieved via a careful analysis of the critical local cohomology modules. The vanishing theorems that we prove are sharp in various respects.
Cite
@article{arxiv.2509.20470,
title = {The arithmetic rank of determinantal nullcones},
author = {Jack Jeffries and Vaibhav Pandey and Anurag K. Singh and Uli Walther},
journal= {arXiv preprint arXiv:2509.20470},
year = {2026}
}
Comments
Substantially improved results on symmetric determinantal nullcones (Section 5); new techniques added in Section 2 that streamline several proofs