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.
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 .
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...
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...
For some values of the degrees of the equations, we show, using geometric invariant theory, that the coarse moduli space of smooth complete intersections in is quasi-projective.
On considère une extension finie de , avec un nombre premier, un sous-groupe d’indice fini de et le groupe . Nous montrons que admet un sous-groupe -Zariski-dense dont toutes les matrices ont leur spectre inclus dans si et seulement si soit est dans le sous-groupe , soit n’est pas congru à 2 modulo 4.