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Singular Locus of a Schubert Variety in the Flag Variety SLn/B
In this chapter, we present the results on the singular locus of a Schubert variety in the flag variety. For an in-depth discussion on the singular...
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A rim-hook rule for quiver flag varieties
The Abelian/non-Abelian correspondence for cohomology (Martin in Symplectic quotients by a nonabelian group and by its maximal torus.
ar**v:math/0001002... 
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On the Seshadri constants of equivariant bundles over Bott–Samelson varieties and wonderful compactifications
We study torus-equivariant vector bundles E on a complex projective variety X which is either a Bott–Samelson–Demazure–Hansen variety or a wonderful...
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On the Geometry of the Anti-canonical Bundle of the Bott-Samelson-Demazure-Hansen Varieties
Let G be a semi-simple simply connected algebraic group over the field ℂ of complex numbers. Let T be a maximal torus of G , and let W be the Weyl...
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A local model for the trianguline variety and applications
We describe the completed local rings of the trianguline variety at certain points of integral weights in terms of completed local rings of algebraic...
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Divided symmetrization and quasisymmetric functions
Motivated by a question in Schubert calculus, we study the interplay of quasisymmetric polynomials with the divided symmetrization operator, which...
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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...
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The Gromov Width of Bott-Samelson Varieties
We prove that the Gromov width of any Bott-Samelson variety associated to a reduced expression and equipped with a rational Kähler form equals the...
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Lattice Path Matroids and Quotients
We characterize the quotients among lattice path matroids (LPMs) in terms of their diagrams. This characterization allows us to show that ordering...
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Three Takes on Almost Complete Intersection Ideals of Grade 3
We are interested in the structure of almost complete intersection ideals of grade 3. We give three constructions of these ideals and their free...
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AN ADDITIVE BASIS FOR THE COHOMOLOGY RINGS OF REGULAR NILPOTENT HESSENBERG VARIETIES
In this paper we construct an additive basis for the cohomology ring of a regular nilpotent Hessenberg variety which is obtained by extending all...
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Transition formulas for involution Schubert polynomials
The orbits of the orthogonal and symplectic groups on the flag variety are in bijection, respectively, with the involutions and fixed-point-free...
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Greatest Ricci lower bounds of projective horospherical manifolds of Picard number one
A horospherical variety is a normal G -variety such that a connected reductive algebraic group G acts with an open orbit isomorphic to a torus bundle...
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The Grassmannian of affine subspaces
The Grassmannian of affine subspaces is a natural generalization of both the Euclidean space, points being 0-dimensional affine subspaces, and the...
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CRYSTAL STRUCTURES FOR SYMMETRIC GROTHENDIECK POLYNOMIALS
The symmetric Grothendieck polynomials representing Schubert classes in the K theory of Grassmannians are generating functions for semistandard...
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P-flag spaces and incidence stratifications
For any finite poset P , we introduce a homogeneous space as a quotient of the general linear group. When P is a chain this quotient is a complete...
