Deformations of affine torus varieties.
Degeneration of Schubert varieties of to toric varieties
Using the polytopes defined in an earlier paper, we show in this paper the existence of degeneration of a large class of Schubert varieties of to toric varieties by extending the method used by Gonciulea and Lakshmibai for a miniscule to Schubert varieties in .
Degrés d’homogénéité de l’ensemble des intersections complètes singulières
Un résultat classique de Boole montre que, sur un corps de caractéristique 0, l’ensemble des hypersurfaces singulières de degré dans est un diviseur de degré de l’espace projectif de toutes les hypersurfaces. On obtient ici des formules analogues pour des intersections complètes de codimension et de degrés quelconques dans , en toute caractéristique.
Derived category of toric varieties with small Picard number
This paper aims to construct a full strongly exceptional collection of line bundles in the derived category D b(X), where X is the blow up of ℙn−r ×ℙr along a multilinear subspace ℙn−r−1×ℙr−1 of codimension 2 of ℙn−r ×ℙr. As a main tool we use the splitting of the Frobenius direct image of line bundles on toric varieties.
Describing toric varieties and their equivariant cohomology
Topologically, compact toric varieties can be constructed as identification spaces: they are quotients of the product of a compact torus and the order complex of the fan. We give a detailed proof of this fact, extend it to the non-compact case and draw several, mostly cohomological conclusions. In particular, we show that the equivariant integral cohomology of a toric variety can be described in terms of piecewise polynomials on the fan if the ordinary integral cohomology is concentrated in even...
Dilogarithm, grassmannian complex and scissors congruence groups of algebraic polyhedra
Discrete polymatroids.
Divisorial cohomology vanishing on toric varieties.