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arXiv · 2608.29445

The arithmetic rank of nullcones of classical invariant rings

Manav Batavia·Aryaman Maithani·Kesavan Mohana Sundaram
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Abstract

We compute the arithmetic rank of nullcone ideals arising from natural actions of the special linear, orthogonal, and symplectic groups on direct sums of copies of their standard and dual representations. Over an infinite field of characteristic different from two, we show that the arithmetic rank equals the Krull dimension of the invariant ring, and compute this dimension. In positive characteristic, the required lower bounds are not detected by local cohomology, and are obtained using \'etale cohomology.

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Manav Batavia, Aryaman Maithani, Kesavan Mohana Sundaram. 2026-08-29. The arithmetic rank of nullcones of classical invariant rings. https://arxiv.org/abs/2608.29445

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