The arithmetic rank of determinantal nullcones

Fuente: arXiv
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Main Authors: Jeffries, Jack, Pandey, Vaibhav, Singh, Anurag K., Walther, Uli
Format: Preprint
Published: 2025
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_version_ 1866917277313531904
author Jeffries, Jack
Pandey, Vaibhav
Singh, Anurag K.
Walther, Uli
author_facet Jeffries, Jack
Pandey, Vaibhav
Singh, Anurag K.
Walther, Uli
contents We compute the arithmetic rank as well as the local/étale 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.
format Preprint
id arxiv_https___arxiv_org_abs_2509_20470
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle The arithmetic rank of determinantal nullcones
Jeffries, Jack
Pandey, Vaibhav
Singh, Anurag K.
Walther, Uli
Commutative Algebra
Algebraic Geometry
Representation Theory
Primary 13A50, Secondary 13C40, 13D45, 13F20, 14F20, 55N10
We compute the arithmetic rank as well as the local/étale 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.
title The arithmetic rank of determinantal nullcones
topic Commutative Algebra
Algebraic Geometry
Representation Theory
Primary 13A50, Secondary 13C40, 13D45, 13F20, 14F20, 55N10
url https://arxiv.org/abs/2509.20470