3-Instantons et réseaux de quadriques.
A Barth-Lefschetz type theorem for branched coverings of Grassmannians.
A class of n-bundles on Gr (k, n).
A classification of the nilpotent triangular matrices
A classification theorem on Fano bundles
In this paper we classify rank two Fano bundles on Fano manifolds satisfying . The classification is obtained via the computation of the nef and pseudoeffective cones of the projectivization , that allows us to obtain the cohomological invariants of and . As a by-product we discuss Fano bundles associated to congruences of lines, showing that their varieties of minimal rational tangents may have several linear components.
A derivation of Kohnert's algorithm from Monk's rule.
A description based on Schubert classes of cohomology of flag manifolds
We describe the integral cohomology rings of the flag manifolds of types Bₙ, Dₙ, G₂ and F₄ in terms of their Schubert classes. The main tool is the divided difference operators of Bernstein-Gelfand-Gelfand and Demazure. As an application, we compute the Chow rings of the corresponding complex algebraic groups, recovering thereby the results of R. Marlin.
A Hessenberg generalization of the Garsia-Procesi basis for the cohomology ring of Springer varieties.
A modular compactification of the general linear group.
A normal form for curves in Grassmannians.
A note on Schubert varieties in G / B.
A Pieri-Chevalley formula in the K-theory of a -bundle.
A Pieri-type formula for even orthogonal Grassmannians
We study the cohomology ring of the Grassmannian G of isotropic n-subspaces of a complex 2m-dimensional vector space, endowed with a nondegenerate orthogonal form (here 1 ≤ n < m). We state and prove a formula giving the Schubert class decomposition of the cohomology products in H*(G) of general Schubert classes by "special Schubert classes", i.e. the Chern classes of the dual of the tautological vector bundle of rank n on G. We discuss some related properties of reduced decompositions of "barred...
A Pieri-type theorem for Lagrangian and odd Orthogonal Grassmannians.
A simultaneous Frobenius splitting for closures of conjugacy classes of nilpotent matrices
A triple intersection theorem for the varieties SO(n)/Pd
We study the Schubert calculus on the space of d-dimensional linear subspaces of a smooth n-dimensional quadric lying in the projective space. Following Hodge and Pedoe we develop the intersection theory of this space in a purely combinatorial manner. We prove in particular that if a triple intersection of Schubert cells on this space is nonempty then a certain combinatorial relation holds among the Schubert symbols involved, similar to the classical one. We also show when these necessary conditions...
A Vanishing Theorem for Group Compactifications.
A Very Simple Proof of Bott's Theorem.
Abel's Theorem and Webs.
Affine braid group actions on derived categories of Springer resolutions
In this paper we construct and study an action of the affine braid group associated with a semi-simple algebraic group on derived categories of coherent sheaves on various varieties related to the Springer resolution of the nilpotent cone. In particular, we describe explicitly the action of the Artin braid group. This action is a “categorical version” of Kazhdan-Lusztig-Ginzburg’s construction of the affine Hecke algebra, and is used in particular by the first author and I. Mirković in the course...