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Schubert Calculus on Newton–Okounkov Polytopes
A Newton–Okounkov polytope of a complete flag variety can be turned into a convex geometric model for Schubert calculus. Namely, we can represent...
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Schubert varieties in the Grassmannian and the symplectic Grassmannian via a bounded RSK correspondence
In a paper by Kodiyalam and Raghavan, they provide an explicit combinatorial description of the Hilbert function of the tangent cone at any point on...
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A Positive Formula for Type A Peterson Schubert Calculus
The Peterson variety is a special case of a nilpotent Hessenberg variety, a class of subvarieties of G / B that have appeared in the study of quantum...
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On the cohomology rings of real flag manifolds: Schubert cycles
We give an algorithm to compute the integer cohomology groups of any real partial flag manifold, by computing the incidence coefficients of the...
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Classification of Schubert Galois Groups in \(\textit{Gr}\,(4,9)\)
We classify Schubert problems in the Grassmannian of 4-planes in 9-dimensional space by their Galois groups. Of the 31,806 essential Schubert...
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Structure constants for Chern classes of Schubert cells
A formula for the structure constants of the multiplication of Schubert classes is obtained in (Rebecca and Allen. ar**v preprint
ar**v:1909.05283 ... -
QUANTUM TORIC DEGENERATION OF QUANTUM FLAG AND SCHUBERT VARIETIES
We show that certain homological regularity properties of graded connected algebras, such as being AS-Gorenstein or AS-Cohen–Macaulay, can be tested...
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Elliptic classes of Schubert varieties
We introduce new notions in elliptic Schubert calculus: the (twisted) Borisov–Libgober classes of Schubert varieties in general homogeneous spaces G / P ...
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Random walks on linear groups satisfying a Schubert condition
We study random walks on GL d (ℝ) whose proximal dimension r is larger than 1 and whose limit set in the Grassmannian Gr r,d (ℝ) is not contained any...
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DEGENERATE SCHUBERT VARIETIES IN TYPE A
We introduce rectangular elements in the symmetric group. In the framework of PBW degenerations, we show that in type A the degenerate Schubert...
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Seshadri stratifications and standard monomial theory
We introduce the notion of a Seshadri stratification on an embedded projective variety. Such a structure enables us to construct a Newton-Okounkov...
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BOTT–SAMELSON–DEMAZURE–HANSEN VARIETIES FOR PROJECTIVE HOMOGENEOUS VARIETIES WITH NONREDUCED STABILIZERS
Over a field of positive characteristic, a semisimple algebraic group G may have some nonreduced parabolic subgroup P . In this paper, we study the...
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Toroidal Schubert Varieties
Levi subgroup actions on Schubert varieties are studied. In the case of partial flag varieties, the horospherical actions are determined. This leads...
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ħ-Deformed Schubert Calculus in Equivariant Cohomology, K-Theory, and Elliptic Cohomology
In this survey paper we review recent advances in the calculus of Chern-Schwartz-MacPherson, motivic Chern, and elliptic classes of classical...
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PBW Degenerate Schubert Varieties: Cartan Components and Counterexamples
In recent years PBW degenerations of Demazure modules and Schubert varieties were defined and studied in several papers. Various interesting...
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On the Continuity of the Tangent Cone to the Determinantal Variety
Tangent and normal cones play an important role in constrained optimization to describe admissible search directions and, in particular, to formulate...