From Schubert Varieties to Doubly-Spherical Varieties

TL;DR

This paper explores the structure of Schubert varieties, introduces doubly spherical varieties, and demonstrates that nearly toric Schubert varieties are doubly spherical, expanding understanding of their algebraic and geometric properties.

Contribution

It introduces doubly spherical varieties and establishes their relation to nearly toric Schubert varieties, providing new insights into their structure.

Findings

Stabilizer of points in Schubert varieties is strongly solvable.

Connectedness of stabilizer subgroups is analyzed.

Nearly toric Schubert varieties are shown to be doubly spherical.

Abstract

Horospherical Schubert varieties are determined. It is shown that the stabilizer of an arbitrary point in a Schubert variety is a strongly solvable algebraic group. The connectedness of this stabilizer subgroup is discussed. Moreover, a new family of spherical varieties, called doubly spherical varieties, is introduced. It is shown that every nearly toric Schubert variety is doubly spherical.