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.
Classification of spherical varieties
We give a short introduction to the problem of classification of spherical varieties, by presenting the Luna conjecture about the classification of wonderful varieties and illustrating some of the related currently known results.
Classification of strict wonderful varieties
In the setting of strict wonderful varieties we prove Luna’s conjecture, saying that wonderful varieties are classified by combinatorial objects, the so-called spherical systems. In particular, we prove that primitive strict wonderful varieties are mostly obtained from symmetric spaces, spherical nilpotent orbits and model spaces. To make the paper as self-contained as possible, we also gather some known results on these families and more generally on wonderful varieties.
Closures of Conjugacy Classes of Matrices are Normal.
Clusters of infinitely near points.
Cohen-Macaulayness of modules of covariants.
Cohomologie des fibrés en droites sur les compactifications des groupes réductifs
Cohomologie des groupes et corps d'invariants multiplicatifs.
Cohomologie équivariante des points semi-stables.
Cohomology of projective varieties with regular SL2 actions.
Cohomology of the G-Hilbert Scheme for 1/r(1,1,R−1)
2000 Mathematics Subject Classification: Primary 14E15; Secondary 14C05,14L30.In this note we attempt to generalize a few statements drawn from the 3-dimensional McKay correspondence to the case of a cyclic group not in SL(3, C). We construct a smooth, discrepant resolution of the cyclic, terminal quotient singularity of type 1/r(1,1,r−1), which turns out to be isomorphic to Nakamura’s G-Hilbert scheme. Moreover we explicitly describe tautological bundles and use them to construct a dual basis to...
Commutative and noncommutative invariant theory
Compactification des variétés de Deligne-Lusztig
Nous construisons explicitement la normalisation de la compactification de Bott-Samelson-Demazure-Hansen des variétés de Deligne-Lusztig dans leur revêtement et retrouvons ainsi un résultat de Deligne-Lusztig sur la monodromie locale autour des diviseurs de la compactification.
Complex analytic geometry of complex parallelizable manifolds