Semi-stability of reductive group schemes over curves.
Separeted orbits for certain non-reductive subgroups.
Series of nilpotent orbits.
Seshadri constants and interpolation on commutative algebraic groups
In this article we study interpolation estimates on a special class of compactifications of commutative algebraic groups constructed by Serre. We obtain a large quantitative improvement over previous results due to Masser and the first author and our main result has the same level of accuracy as the best known multiplicity estimates. The improvements come both from using special properties of the compactifications which we consider and from a different approach based upon Seshadri constants and...
Simple models of quasihomogeneous projective 3-folds.
Singular localization of -modules and applications to representation theory
We prove a singular version of Beilinson–Bernstein localization for a complex semi-simple Lie algebra following ideas from the positive characteristic case settled by [BMR06]. We apply this theory to translation functors, singular blocks in the Bernstein–Gelfand–Gelfand category O and Whittaker modules.
Singular Moment Maps and Quaternionic Geometry
Singular principal -bundles on nodal curves
In the present paper, we give a first general construction of compactified moduli spaces for semistable -bundles on an irreducible complex projective curve with exactly one node, where is a semisimple linear algebraic group over the complex numbers.
Singularités de Klein - I
Singularités de Klein - II
Singularites rationnelles et quotients par les groupes reductifs.
Singularities of affine Schubert varieties.
Singularities of Closures of K-orbits on Flag Manifolds.
Singularities of Quotients by Vector Fields in Characteristic p.
-equivariant polynomial automorphisms of the binary forms
We consider the space of binary forms of degree denoted by . We will show that every polynomial automorphism of which commutes with the linear -action and which maps the variety of forms with pairwise distinct zeroes into itself, is a multiple of the identity on .
SL2 actions and cohomology of Schubert varieties
Smallness problem for quantum affine algebras and quiver varieties
The geometric small property (Borho-MacPherson [2]) of projective morphisms implies a description of their singularities in terms of intersection homology. In this paper we solve the smallness problem raised by Nakajima [37, 35] for certain resolutions of quiver varieties [37] (analogs of the Springer resolution): for Kirillov-Reshetikhin modules of simply-laced quantum affine algebras, we characterize explicitly the Drinfeld polynomials corresponding to the small resolutions. We use an elimination...
Smooth components of Springer fibers
This article studies components of Springer fibers for that are associated to closed orbits of on the flag variety of . These components occur in any Springer fiber. In contrast to the case of arbitrary components, these components are smooth varieties. Using results of Barchini and Zierau we show these components are iterated bundles and are stable under the action of a maximal torus of . We prove that if is a line bundle on the flag variety associated to a dominant weight, then the higher...
Solving the sextic by iteration: a study in complex geometry and dynamics.
Some model theory of simple algebraic groups over algebraically closed fields