Schubert functions and the number of reduced words of permutations.
Schubert varieties and Demazure's character formula.
Schubert varieties and representations of Dynkin quivers
We show that the types of singularities of Schubert varieties in the flag varieties Flagₙ, n ∈ ℕ, are equivalent to the types of singularities of orbit closures for the representations of Dynkin quivers of type 𝔸. Similarly, we prove that the types of singularities of Schubert varieties in products of Grassmannians Grass(n,a) × Grass(n,b), a, b, n ∈ ℕ, a, b ≤ n, are equivalent to the types of singularities of orbit closures for the representations of Dynkin quivers of type 𝔻. We also show that...
Schubert varieties and standard monomial theory
Schubert varieties are arithmetically Cohen-Macaulay.
Schubert varieties in
Schubert varieties, toric varieties and ladder determinantal varieties
We construct certain normal toric varieties (associated to finite distributive lattices) which are degenerations of the Grassmannians. We also determine the singular loci for certain normal toric varieties, namely the ones which are certain ladder determinantal varieties. As a consequence, we prove a refined version of the conjecture of Laksmibai & Sandhya [Criterion for smoothness of Schubert varieties in , Proc. Ind. Acad. Sci., 100 (1990), 45-52] on the components of the singular locus,...
Schur and Schubert polynomials as Thom polynomials-cohomology of moduli spaces
The theory of Schur and Schubert polynomials is revisited in this paper from the point of view of generalized Thom polynomials. When we apply a general method to compute Thom polynomials for this case we obtain a new definition for (double versions of) Schur and Schubert polynomials: they will be solutions of interpolation problems.
Singular components of Springer fibers in the two-column case
We consider the Springer fiber corresponding to a nilpotent endomorphism of nilpotent order . As a first result, we give a description of the elements of a given component of which are fixed by the action of the standard torus relative to some Jordan basis of . By using this result, we establish a necessary and sufficient condition of singularity for the components of .
Singularités génériques des variétés de Schubert covexillaires
On montre que les composantes irréductibles du lieu singulier d’une variété de Schubert dans associée à une permutation covexillaire, sont paramétrées par certains des points coessentiels du graphe de la permutation. On donne une description explicite de ces composantes et l’on décrit la singularité le long de chacune d’entre elles.
Singularities of affine Schubert varieties.
Singularities of Closures of K-orbits on Flag Manifolds.
Singularities on flag spaces
SL2 actions and cohomology of Schubert varieties
Slices étales
Smooth components of Springer fibers
This article studies components of Springer fibers for that are associated to closed orbits of on the flag variety of . These components occur in any Springer fiber. In contrast to the case of arbitrary components, these components are smooth varieties. Using results of Barchini and Zierau we show these components are iterated bundles and are stable under the action of a maximal torus of . We prove that if is a line bundle on the flag variety associated to a dominant weight, then the higher...
Smooth surfaces of degree 9 in G(1,3).
Smoothness and irreducibility of varieties of plane curves with nodes and cusps
Some Properties of Stahle Rank-2 Vector Bundles on Pn.
Some remarks on morphisms between Fano threefolds.