2025/12/03 by Lee, Jaehoon, Park, Sangwoo, Yeon, Eungbeom
#53A10 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #Differential Geometry (math.DG) #FOS: Mathematics
paper · doi:10.48550/arxiv.2512.03480
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.