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Theoretical analysis reveals complete nonsingularity and solvable stabilizer structures in horospherical Schubert varieties, indicating preserved symmetry in algebraic varieties.
The algebraic group structure of stabilizers of points in Schubert varieties is investigated. We show that these stabilizers are always strongly solvable algebraic groups and discuss their connectedness properties. Furthermore, we provide a complete characterization of horospherical Schubert varieties and prove that every horospherical Schubert variety is nonsingular. We also introduce a new class of spherical varieties, which we call doubly-spherical varieties, and show that all nearly toric Schubert varieties belong to this family.
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Can et al. (2026) studied this question.
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