Group actions on Jacobian varieties.
Groupes de Cremona, connexité et simplicité
Le groupe de Cremona est connexe en toute dimension et, muni de sa topologie, il est simple en dimension .
Harder-Narasimhan filtrations and optimal destabilizing vectors in complex geometry
We give here a generalization of the theory of optimal destabilizing 1-parameter subgroups to non algebraic complex geometry : we consider holomorphic actions of a complex reductive Lie group on a finite dimensional (possibly non compact) Kähler manifold. In a second part we show how these results may extend in the gauge theoretical framework and we discuss the relation between the Harder-Narasimhan filtration and the optimal detstabilizing vectors of a non semistable object....
Higher-Dimensional Analogues of Inoue-Hirzebruch Surfaces.
Hilbert's Fourteenth Problem for Non-Reductive Groups.
Hodge groups of K3 surfaces.
Holomorphic equivariant cohomology.
Homogeneous Complex Surfaces.
Homogeneous polynomials with isomorphic Milnor algebras
We recall first Mather's Lemma providing effective necessary and sufficient conditions for a connected submanifold to be contained in an orbit. We show that two homogeneous polynomials having isomorphic Milnor algebras are right-equivalent.
Homogeneous varieties for semisimple groups of rank one
Homological dimension of algebras of invariants.
Homology of the Steinberg variety and Weyl group coinvariants.
Hyperdéterminant d’un -homomorphisme
Etant donnés () des -modules non triviaux de dimensions respectives (avec ) et un -homomorphisme, nous montrons que l’hyperdéterminant de est nul sauf si les modules sont irréductibles et si l’homomorphisme est la multiplication des polynômes homogènes à deux variables.
Immersions of module varieties
We show that a homomorphism of algebras is a categorical epimorphism if and only if all induced morphisms of the associated module varieties are immersions. This enables us to classify all minimal singularities in the subvarieties of modules from homogeneous standard tubes.
Inequalities defining orbit spaces.
Infinite Root Systems, Representations of Graphs and Invariant Theory.
Introduction to actions of algebraic groups
These notes present some fundamental results and examples in the theory of algebraic group actions, with special attention to the topics of geometric invariant theory and of spherical varieties. Their goal is to provide a self-contained introduction to more advanced lectures.
Invariant differential operators and Frobenius decomposition of a -variety. (Invariante Differentialoperatoren und die Frobenius-Zerlegung einer -Varietät.)
Invariant differential operators on symplectic Grassmann manifolds.
Invariant differential operators on the tangent space of some symmetric spaces
Let be a complex, semisimple Lie algebra, with an involutive automorphism and set , . We consider the differential operators, , on that are invariant under the action of the adjoint group of . Write for the differential of this action. Then we prove, for the class of symmetric pairs considered by Sekiguchi, that . An immediate consequence of this equality is the following result of Sekiguchi: Let be a real form of one of these symmetric pairs , and suppose that is a -invariant...