Eisenstein series on reductive symmetric spaces and representations of Hecke algebras.
Elliptic curves on spinor varieties
We prove irreducibility of the scheme of morphisms, of degree large enough, from a smooth elliptic curve to spinor varieties. We give an explicit bound on the degree.
Equivariant principal bundles for G–actions and G–connections
Given a complex manifold M equipped with an action of a group G, and a holomorphic principal H–bundle EH on M, we introduce the notion of a connection on EH along the action of G, which is called a G–connection. We show some relationship between the condition that EH admits a G–equivariant structure and the condition that EH admits a (flat) G–connection. The cases of bundles on homogeneous spaces and smooth toric varieties are discussed.
Erratum: Complexity and rank double cones and tensor products decompositions.
Erratum : On the Hasse principle for homogeneous spaces with finite stabilizers
Espaces homogènes et arithmétique des schémas en groupes réductifs sur les anneaux de Dedekind
Soit un schéma arithmétique de dimension , c’est-à-dire le spectre de l’anneau des entiers d’un corps de nombres ou une courbe algébrique, lisse, irréductible, définie sur un corps fini ou algébriquement clos. Nous associons à un -espace homogène (à gauche) d’un groupe réductif dont l’isotropie est aussi un groupe réductif une classe caractéristique qui, dans le cas où est semi-simple, vit dans un de à valeurs dans le noyau du revêtement universel d’une -forme de . Cette classe...
Espaces homogenes spheriques.
Espaces principaux homogènes localement triviaux
Éventails et variétés toriques
Exterior differential systems, Lie algebra cohomology, and the rigidity of homogenous varieties
These are expository notes from the 2008 Srní Winter School. They have two purposes: (1) to give a quick introduction to exterior differential systems (EDS), which is a collection of techniques for determining local existence to systems of partial differential equations, and (2) to give an exposition of recent work (joint with C. Robles) on the study of the Fubini-Griffiths-Harris rigidity of rational homogeneous varieties, which also involves an advance in the EDS technology.
Extremal plurisubharmonic functions of linear growth on algebraic varieties.