The topological nature of algebraic contractions
The transversality of a general translate
The universal rank-(n-1) bundle on G(i,n) restricted to subvarieties.
We classify those smooth (n-1)-folds in G(1,Pn) for which the restriction of the rank-(n-1) universal bundle has more than n+1 independent sections. As an application, we classify also those (n-1)-folds for which that bundle splits.
Théorèmes de Lefschetz pour les lieux de dégénérescence
Total positivity for cominuscule Grassmannians.
Twisted action of the symmetric group on the cohomology of a flag manifold
Classes dual to Schubert cycles constitute a basis on the cohomology ring of the flag manifold F, self-adjoint up to indexation with respect to the intersection form. Here, we study the bilinear form (X,Y) :=〈X·Y, c(F)〉 where X,Y are cocycles, c(F) is the total Chern class of F and〈,〉 is the intersection form. This form is related to a twisted action of the symmetric group of the cohomology ring, and to the degenerate affine Hecke algebra. We give a distinguished basis for this form, which is a...