Minimal Singularities in GLn.
Moduli spaces of decomposable morphisms of sheaves and quotients by non-reductive groups
We extend the methods of geometric invariant theory to actions of non–reductive groups in the case of homomorphisms between decomposable sheaves whose automorphism groups are non–reductive. Given a linearization of the natural action of the group on Hom(E,F), a homomorphism is called stable if its orbit with respect to the unipotent radical is contained in the stable locus with respect to the natural reductive subgroup of the automorphism group. We encounter effective numerical conditions for...
Moduli-stacks for bundles on semistable curves.
Monodromy of functions defined on isolated singularities of complete intersections
Naive boundary strata and nilpotent orbits
We give a Hodge-theoretic parametrization of certain real Lie group orbits in the compact dual of a Mumford-Tate domain, and characterize the orbits which contain a naive limit Hodge filtration. A series of examples are worked out for the groups , , and .
Nef value of homogeneous line bundles and related vanishing theorems.
Normale Einbettungen von G..U .
Normality and non-normality of group compactifications in simple projective spaces
Given an irreducible representation of a complex simply connected semisimple algebraic group we consider the closure of the image of in . We determine for which the variety is normal and for which is smooth.
Normes -adiques et extensions quadratiques
On classifie les orbites de sur l’immeuble de Bruhat-Tits de pour trois paires sphériques de groupes -adiques classiques.
Oka manifolds: From Oka to Stein and back
Oka theory has its roots in the classical Oka-Grauert principle whose main result is Grauert’s classification of principal holomorphic fiber bundles over Stein spaces. Modern Oka theory concerns holomorphic maps from Stein manifolds and Stein spaces to Oka manifolds. It has emerged as a subfield of complex geometry in its own right since the appearance of a seminal paper of M. Gromov in 1989.In this expository paper we discuss Oka manifolds and Oka maps. We describe equivalent characterizations...
On Almost Homogeneous Compact Complex Analytic Surfaces.
On complete orbit spaces of SL(2) actions
On complete orbit spaces of SL(2) actions, II
The aim of this paper is to extend the results of [BB-Ś2] concerning geometric quotients of actions of SL(2) to the case of good quotients. Thus the results of the present paper can be applied to any action of SL(2) on a complete smooth algebraic variety, while the theorems proved in [BB-Ś2] concerned only special situations.
On deformation method in invariant theory
In this paper we relate the deformation method in invariant theory to spherical subgroups. Let be a reductive group, an affine -variety and a spherical subgroup. We show that whenever is affine and its semigroup of weights is saturated, the algebra of -invariant regular functions on has a -invariant filtration such that the associated graded algebra is the algebra of regular functions of some explicit horospherical subgroup of . The deformation method in its usual form, as developed...
On existence of double coset varieties
Let G be a complex affine algebraic group and H,F ⊂ G be closed subgroups. The homogeneous space G/H can be equipped with the structure of a smooth quasiprojective variety. The situation is different for double coset varieties F∖∖G//H. We give examples showing that the variety F∖∖G//H does not necessarily exist. We also address the question of existence of F∖∖G//H in the category of constructible spaces and show that under sufficiently general assumptions F∖∖G//H does exist as a constructible space....
On functional equations of complex powers.
On Harder-Narashimhan stratification over Quot schemes.
On Manifolds Locally Modelled on Non-Riemannian Homogeneous Spaces.
On quasihomogeneous manifolds – via Brion-Luna-Vust theorem
We consider a smooth projective variety on which a simple algebraic group acts with an open orbit. We discuss a theorem of Brion-Luna-Vust in order to relate the action of with the induced action of on the normal bundle of a closed orbit of the action. We get effective results in case and .
On set theoretic complete intersections in P3k.