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arXiv · 2310.18925

Total positivity for matroid Schubert varieties

Xuhua He·Connor Simpson·Kaitao Xie
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Abstract

We define the totally nonnegative matroid Schubert variety $\mathcal Y_V$ of a linear subspace $V \subset \mathbb R^n$. We show that $\mathcal Y_V$ is a regular CW complex homeomorphic to a closed ball, with strata indexed by pairs of acyclic flats of the oriented matroid of $V$. This closely resembles the regularity theorem for totally nonnegative generalized flag varieties. As a corollary, we obtain a regular CW structure on the real matroid Schubert variety of $V$.

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Xuhua He, Connor Simpson, Kaitao Xie. 2023-10-29. Total positivity for matroid Schubert varieties. https://arxiv.org/abs/2310.18925

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