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Standard monomial theory and toric degenerations of Richardson varieties inside Grassmannians and flag varieties
We study toric degenerations of opposite Schubert and Richardson varieties inside degenerations of Grassmannians and flag varieties. These degenerations are parametrized by matching fields in theExpand
On intersection cohomology with torus action of complexity one, II
We show that the components, appearing in the decomposition theorem for contraction maps of torus actions of complexity one, are intersection cohomology complexes of even codimensional subvarieties.Expand
Standard monomial theory and toric degenerations of Richardson varieties in flag varieties
We study standard monomial bases for Richardson varieties inside the flag variety. In general, writing down a standard monomial basis for a Richardson variety can be challenging, as it involvesExpand
On the Torus quotients of Schubert varieties
In this paper, we consider the GIT quotients of Schubert varieties for the action of a maximal torus. We describe the minuscule Schubert varieties for which the semistable locus is contained in theExpand
Standard monomial theory and toric degenerations of Richardson varieties in the Grassmannian
Richardson varieties are obtained as intersections of Schubert and opposite Schubert varieties. We provide a new family of toric degenerations of Richardson varieties inside Grassmannians by studyingExpand
The Gromov width of Bott-Samelson varieties
We prove that the Gromov width of any Bott-Samelson variety birational to a Schubert variety and equipped with a rational Kahler form equals the symplectic area of a minimal curve.