An Equivariant Lefschetz Formula for Finite Reductive Groups.
An equivariant Riemann-Roch theorem for complete, simplicial toric varieties.
An extension of Rais' theorem and seaweed subalgebras of simple Lie algebras
We prove an extension of Rais' theorem on the coadjoint representation of certain graded Lie algebras. As an application, we prove that, for the coadjoint representation of any seaweed subalgebra in a general linear or symplectic Lie algebra, there is a generic stabiliser and the field of invariants is rational. It is also shown that if the highest root of a simple Lie algerba is not fundamental, then there is a parabolic subalgebra whose coadjoint representation do not...
An orbit closure for a representation of the Kronecker quiver with bad singularities
We give an example of a representation of the Kronecker quiver for which the closure of the corresponding orbit contains a singularity smoothly equivalent to the isolated singularity of two planes crossing at a point. Therefore this orbit closure is neither Cohen-Macaulay nor unibranch.
Analytic curves in power series rings
Anneaux d'invariants de groupes finis Intersections complètes
Appendix : An example of thick wall
Arithmetisch definierte Gruppen mit Galoisoperation.
Automorphism groups of compact Klein surfaces with one boundary component.
Automorphism groups of the modular curves
Automorphismes et deformations des varietes de Borel
Automorphisms of cusps and Inoue-Hirzebruch surfaces
Automorphisms of Enriques surfaces which act trivially on the cohomology groups.
Catégories dérivées et variétés de Deligne-Lusztig
Challenging problems on affine -space
Characterization of the complex projective space by holomorphic vector fields.
Chern classes of reductive groups and an adjunction formula
In this paper, I construct noncompact analogs of the Chern classes for equivariant vector bundles over complex reductive groups. For the tangent bundle, these Chern classes yield an adjunction formula for the (topological) Euler characteristic of complete intersections in reductive groups. In the case where a complete intersection is a curve, this formula gives an explicit answer for the Euler characteristic and the genus of the curve. I also prove that the higher Chern classes vanish. The first...
Classes d'Euler équivariantes et points rationnellement lisses
Lorsqu’un tore agit sur une variété algébrique complexe munie de la topologie transcendante, nous définissons la classe d’Euler -équivariante d’un point fixe isolé , qu’il soit lisse ou non. Cette classe est une fraction rationnelle à un nombre fini de variables et lorsque est rationnellement lisse dans , c’est un polynôme qui s’identifie canoniquement à la classe d’Euler équivariante usuelle, mais, réciproquement, lorsque la classe d’Euler équivariante est polynomiale, il n’est pas toujours...
Classical Godeaux Surface in Characteristic P.
Classification of low-dimensional orbit closures in varieties of quiver representations
We classify the affine varieties of dimension at most 4 which occur as orbit closures with an invariant point in varieties of representations of quivers. Moreover, we show that they are normal and Cohen-Macaulay.