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PreprintarXiv licencearXiv

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 étale cohomology.

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Cite

BibTeXRIS
BibTeX
@misc{batavia2026arithmetic,
  title = {{The arithmetic rank of nullcones of classical invariant rings}},
  author = {Manav Batavia and Aryaman Maithani and Kesavan Mohana Sundaram},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.29445},
  eprint = {2608.29445},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.29445},
}
RIS
TY  - UNPB
TI  - The arithmetic rank of nullcones of classical invariant rings
AU  - Manav Batavia
AU  - Aryaman Maithani
AU  - Kesavan Mohana Sundaram
PY  - 2026
DA  - 2026/08/29
PB  - arXiv
DO  - 10.48550/arxiv.2608.29445
UR  - https://arxiv.org/abs/2608.29445
AB  - 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 étale cohomology.
ER  -