A Peterson variety is a subvariety of the flag variety G/B defined by certain linear conditions. Peterson varieties appear in the construction of the quantum cohomology of partial flag varieties and in applications to the Toda flows. Each Peterson variety has a one-dimensional torus S acting on it. We give a basis of Peterson Schubert classes for H∗ S1(Pet) and identify the ring generators. In ...

We obtain new combinatorial formulae for modified Hall–Littlewood polynomials, for matrix elements of the transition matrix between the elementary symmetric polynomials and Hall-Littlewood’s ones, and for the number of rational points over the finite field of unipotent partial flag variety. The definitions and examples of generalized mahonian statistic on the set of transport matrices and dual ...

Let D be a holomorphic differential operator acting on sections of a holomorphic vector bundle on an n-dimensional compact complex manifold. We prove a formula, conjectured by Feigin and Shoikhet, giving the Lefschetz number of D as the integral over the manifold of a differential form. The class of this differential form is obtained via formal differential geometry from the canonical generator...

— We study threefolds X ⊂ Pr having as hyperplane section a smooth surface with an elliptic fibration. We first give a general theorem about the possible embeddings of such surfaces with Picard number two. More precise results are then proved for Weierstrass fibrations, both of rank two and higher. In particular we prove that a Weierstrass fibration of rank two that is not a K3 surface is not h...

Cet article présente une recherche sur la négociation collective du télétravail lors de pandémie Covid-19. Sept études cas avec 60 entretiens dans des entreprises secteurs et tailles différenciées montrent diversité mise en place télétravail. Les principaux résultats indiquent culture d’entreprise réfractaire au distanciel, progression importante thème chaque entreprise, négociations difficiles...