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arXiv · 2611.01246

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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Graham Denham, Prajwal Udanshive. 2026-10-31. Resonance varieties of Schubert arrangements. https://arxiv.org/abs/2611.01246

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