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Resonance varieties of Schubert arrangements

  • Graham Denham
  • Prajwal Udanshive
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Abstract

We compute the resonance varieties of the Orlik--Solomon algebras of Schubert matroids. Previously known results have been largely confined to matroids of rank $3$, and the Schubert matroids give a family of nontrivial examples of arbitrary rank. We give an expression for the cohomology of the Orlik--Solomon algebra that we show holds for Schubert matroids as well as for simple, complex-realizable rank-$3$ matroids that do not support multinets. Our proof introduces a family of matroids for which the Orlik--Solomon algebra is isomorphic to an exterior Stanley--Reisner algebra.

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Cite

BibTeXRIS
BibTeX
@misc{denham2026resonance,
  title = {{Resonance varieties of Schubert arrangements}},
  author = {Graham Denham and Prajwal Udanshive},
  howpublished = {arXiv},
  year = {2026},
  month = nov,
  doi = {10.48550/arxiv.2611.01246},
  eprint = {2611.01246},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2611.01246},
}
RIS
TY  - UNPB
TI  - Resonance varieties of Schubert arrangements
AU  - Graham Denham
AU  - Prajwal Udanshive
PY  - 2026
DA  - 2026/11/01
PB  - arXiv
DO  - 10.48550/arxiv.2611.01246
UR  - https://arxiv.org/abs/2611.01246
AB  - We compute the resonance varieties of the Orlik--Solomon algebras of Schubert matroids. Previously known results have been largely confined to matroids of rank $3$, and the Schubert matroids give a family of nontrivial examples of arbitrary rank. We give an expression for the cohomology of the Orlik--Solomon algebra that we show holds for Schubert matroids as well as for simple, complex-realizable rank-$3$ matroids that do not support multinets. Our proof introduces a family of matroids for which the Orlik--Solomon algebra is isomorphic to an exterior Stanley--Reisner algebra.
ER  -