We obtain residue formulae for certain functions of several variables. As an application, we obtain closed formulae for vector partition functions and for their continuous analogs. They imply an… (More)

Given a connected algebraic group G over an algebraically closed field and a G-homogeneous space X , we describe the Chow ring of G and the rational Chow ring of X , with special attention to the… (More)

P (h) φ(x)dx where the polytope P (h) is obtained from P by independent parallel motions of all facets. This extends to simple lattice polytopes the EulerMaclaurin summation formula of Khovanskii and… (More)

Consider the space R∆ of rational functions of r variables with poles on an arrangement of hyperplanes ∆. It is important to study the decomposition of the space R∆ under the action of the ring of… (More)

We prove a conjecture of A. S. Buch concerning the structure constants of the Grothendieck ring of a flag variety with respect to its basis of Schubert structure sheaves. For this, we show that the… (More)

This text is an introduction to equivariant cohomology, a classical tool for topological transformation groups, and to equivariant intersection theory, a much more recent topic initiated by D. Edidin… (More)

A. — We obtain a criterion for rational smoothness of an algebraic variety with a torus action, with applications to orbit closures in flag varieties, and to closures of double classes in… (More)

In these notes, we present some fundamental results concerning flag varieties and their Schubert varieties. By a flag variety, we mean a complex projective algebraic variety X, homogeneous under a… (More)

We obtain a geometric construction of a “standard monomial basis” for the homogeneous coordinate ring associated with any ample line bundle on any flag variety. This basis is compatible with Schubert… (More)

Let X be a normal projective algebraic variety, G its largest connected automorphism group, and A(G) the Albanese variety of G . We determine the isogeny class of A(G) in terms of the geometry of X .… (More)