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arXiv · 2110.08548

Totally nonnegative critical varieties

Pavel Galashin
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Abstract

We study totally nonnegative parts of critical varieties in the Grassmannian. We show that each totally nonnegative critical variety Crit$^{\ge0}_f$ is the image of an affine poset cyclohedron under a continuous map and use this map to define a boundary stratification of Crit$^{\ge0}_f$. For the case of the top-dimensional positroid cell, we show that the totally nonnegative critical variety Crit$^{\ge0}_{k,n}$ is homeomorphic to the second hypersimplex $\Delta_{2,n}$.

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Pavel Galashin. 2021-10-16. Totally nonnegative critical varieties. https://arxiv.org/abs/2110.08548

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