A Characterization of Complex Homogeneous Cones.
A classification of reductive linear groups.
A classification of strictly pseudoconcave homogeneous manifolds
A criterion for extending meromorphic functions.
A general Hilbert-Mumford criterion
Let a reductive group act on an algebraic variety . We give a Hilbert-Mumford type criterion for the construction of open -invariant subsets admitting a good quotient by .
A motivic isomorphism between two projective homogeneous varieties under the action of a group of type . (Un isomorphisme motivique entre deux variétés homogènes projectives sous l'action d'un groupe de type .)
A Pieri-type theorem for Lagrangian and odd Orthogonal Grassmannians.
A recipe for finding open subsets of vector spaces with a good quotient
A refinement of the PRV conjecture.
A restriction theorem and the Poincare series for U-invariants.
A Short Proof of the Kemp Vanishing Theorem.
A Stratification of the Hilbert Scheme of Points in the Projective Plane.
A vanishing theorem for Dolbeault cohomology of homogeneous vector bundles.
A Vanishing Theorem for Group Compactifications.
Adjoint representation of and del Pezzo surfaces of degree
Let be a del Pezzo surface of degree , and let be the simple Lie group of type . We construct a locally closed embedding of a universal torsor over into the -orbit of the highest weight vector of the adjoint representation. This embedding is equivariant with respect to the action of the Néron-Severi torus of identified with a maximal torus of extended by the group of scalars. Moreover, the -invariant hyperplane sections of the torsor defined by the roots of are the inverse images...
Affine compact almost-homogeneous manifolds of cohomogeneity one
This paper is one in a series generalizing our results in [12, 14, 15, 20] on the existence of extremal metrics to the general almost-homogeneous manifolds of cohomogeneity one. In this paper, we consider the affine cases with hypersurface ends. In particular, we study the existence of Kähler-Einstein metrics on these manifolds and obtain new Kähler-Einstein manifolds as well as Fano manifolds without Kähler-Einstein metrics. As a consequence of our study, we also give a solution to the problem...
Algebras with finitely generated invariant subalgebras
We classify all finitely generated integral algebras with a rational action of a reductive group such that any invariant subalgebra is finitely generated. Some results on affine embeddings of homogeneous spaces are also given.
An alternative proof of Scheiderer's theorem on the Hasse principle for principal homogeneous spaces.
Arithmetisch definierte Gruppen mit Galoisoperation.
Automorphisms and local rigidity of regular varieties