Désingularisation des variétés de Schubert généralisées
We propose a theory of double Schubert polynomials for the Lie types , , which naturally extends the family of Lascoux and Schützenberger in type . These polynomials satisfy positivity, orthogonality and stability properties, and represent the classes of Schubert varieties and degeneracy loci of vector bundles. When is a maximal Grassmannian element of the Weyl group, can be expressed in terms of Schur-type determinants and Pfaffians, in analogy with the type formula of Kempf and Laksov....
We prove irreducibility of the scheme of morphisms, of degree large enough, from a smooth elliptic curve to spinor varieties. We give an explicit bound on the degree.
We obtain several several results on the multiplicative structure constants of the T-equivariant Grothendieck ring of the flag variety G/B. We do this by lifting the classes of the structure sheaves of Schubert varieties in to R(T) ⊗ R(T), where R(T) denotes the representation ring of the torus T. We further apply our results to describe the multiplicative structure constants of where X denotes the wonderful compactification of the adjoint group of G, in terms of the structure constants of...
We introduce a new construction of exceptional objects in the derived category of coherent sheaves on a compact homogeneous space of a semisimple algebraic group and show that it produces exceptional collections of the length equal to the rank of the Grothendieck group on homogeneous spaces of all classical groups.