arXiv:2610.35914v1 Announce Type: new Abstract: Let $\mathcal{M}$ be a positroid. We prove that the positroid variety $\Pi_{\mathcal{M}}$ is toric with respect to some algebraic torus if and only if $\mathcal{M}$ is regular. In that case, $\Pi_{\mathcal{M}}$ is toric with respect to the standard diagonal torus. Thus, there are no unexpected toric positroid varieties.
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