On stationary real matrix Schubert varieties

Jaehoon Lee; Sangwoo Park; Eungbeom Yeon

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arXiv · 2512.03480

On stationary real matrix Schubert varieties

Jaehoon Lee·Sangwoo Park·Eungbeom Yeon

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Abstract

In this paper, we study when a real matrix Schubert variety is stationary with respect to the first variation. We first show that a necessary condition for its open dense regular part to be a minimal submanifold is that the corresponding partial permutation is vexillary. Among vexillary partial permutations, we establish minimality by a geometric argument when the Rothe diagram is of Grassmannian type and has at most two connected components. We further obtain, as a corollary, the minimality of those varieties that decompose as products of this type. These varieties include all determinantal varieties as well as some new minimal cones.

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Jaehoon Lee, Sangwoo Park, Eungbeom Yeon. 2025-12-03. On stationary real matrix Schubert varieties. https://arxiv.org/abs/2512.03480

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