On stationary real matrix Schubert varieties
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911299803283456 |
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| author | Lee, Jaehoon Park, Sangwoo Yeon, Eungbeom |
| author_facet | Lee, Jaehoon Park, Sangwoo Yeon, Eungbeom |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_03480 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On stationary real matrix Schubert varieties Lee, Jaehoon Park, Sangwoo Yeon, Eungbeom Differential Geometry Algebraic Geometry Combinatorics 53A10 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. |
| title | On stationary real matrix Schubert varieties |
| topic | Differential Geometry Algebraic Geometry Combinatorics 53A10 |
| url | https://arxiv.org/abs/2512.03480 |