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.
Scrolls and quartics.
Search for homogeneous polynomial invariants and a cubic-homogeneous mapping without quadratic invariants.
Secant spaces and Clifford's theorem
Second Chern class and Riemann-Roch for vector bundles on resolutions of surface singularities.
Second order theta divisors on Pryms
Secondary characteristic classes and intermediate Jacobians.
Sectional genus and cohomology of projective varieties.
Sectional invariants of scroll over a smooth projective variety
Sections des fibrés vectoriels sur une courbe
Sections des fibrés vectoriels sur une courbe
Sections du fibré déterminant sur l'espace de modules des faisceaux semi-stables de rang 2 sur le plan projectif
La conjecture de “dualité étrange” de Le Potier donne un isomorphisme entre l’espace des sections du fibré déterminant sur deux espaces de modules différents de faisceaux semi-stables sur le plan projectif . Si on considère deux classes orthogonales dans l’algèbre de Grothendieck telles que est de rang strictement positif et est de rang zéro, on note et les espaces de modules de faisceaux semi-stables de classe , respectivement , sur . Il existe sur (resp. ) un fibré déterminant...
Segre-Veronese embeddings of P1 x P1 x P1 and their secant varieties.
In this paper we compute the dimension of all the sth higher secant varieties of the Segre-Veronese embeddings Yd of the product P1 × P1 × P1 in the projective space PN via divisors of multidegree d = (a,b,c) (N = (a+1)(b+1)(c+1) - 1). We find that Yd has no deficient higher secant varieties, unless d = (2,2,2) and s = 7, or d = (2h,1,1) and s = 2h + 1, with defect 1 in both cases.