Equivariant degenerations of spherical modules for groups of type $\mathsf {A}$

Papadakis, Stavros Argyrios; Van Steirteghem, Bart

doi:10.5802/aif.2735

Equivariant degenerations of spherical modules for groups of type

A

[Les dégénérescences équivariantes des modules sphériques de type

A

]

Papadakis, Stavros Argyrios ¹ ; Van Steirteghem, Bart ²

¹ Universidade Técnica de Lisboa Centro de Análise Matemática Geometria e Sistemas Dinâmicos Departamento de Matemática Instituto Superior Técnico Av. Rovisco Pais 1049-001 Lisboa (Portugal)
² Medgar Evers College Department of Mathematics City University of New York 1650 Bedford Ave. Brooklyn, NY 11225 (USA)

Annales de l'Institut Fourier, Tome 62 (2012) no. 5, pp. 1765-1809.

Résumé
Abstract

V. Alexeev et M. Brion ont introduit, pour un groupe complexe réductif donné, un schéma de modules de variétés sphériques affines ayant le même semi-groupe moment. Nous donnons de nouveaux exemples de ce schéma de modules en montrant qu’il est un espace affine lorsque le groupe donné est de type $A$ et le semi-groupe moment fixé est celui d’un module sphérique.

V. Alexeev and M. Brion introduced, for a given a complex reductive group, a moduli scheme of affine spherical varieties with prescribed weight monoid. We provide new examples of this moduli scheme by proving that it is an affine space when the given group is of type $A$ and the prescribed weight monoid is that of a spherical module.

EuDML MR Zbl

DOI : 10.5802/aif.2735

Classification : 14D22, 14C05, 14M27, 20G05
Keywords: Invariant Hilbert scheme, spherical module, spherical variety, equivariant degeneration
Mot clés : schéma de Hilbert invariant, module sphérique, variété sphérique, dégénérescence équivariante

Affiliations des auteurs :

Papadakis, Stavros Argyrios ¹ ; Van Steirteghem, Bart ²

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     journal = {Annales de l'Institut Fourier},
     pages = {1765--1809},
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Papadakis, Stavros Argyrios; Van Steirteghem, Bart. Equivariant degenerations of spherical modules for groups of type $\mathsf {A}$. Annales de l'Institut Fourier, Tome 62 (2012) no. 5, pp. 1765-1809. doi : 10.5802/aif.2735. http://www.numdam.org/articles/10.5802/aif.2735/

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