ON THE GENERALIZED COMMUTING VARIETIES OF A REDUCTIVE LIE ALGEBRA

Jean-Yves Charbonnel (1) , Mouchira Zaiter (1)

1 IMJ - Institut de Mathématiques de Jussieu

The generalized commuting and isospectral commuting varieties of a reductive Lie algebra have been introduced in a preceding article. In this note, it is proved that their normalizations are Gorenstein with rational singularities. Moreover, their canonical modules are free of rank 1. In particular, the usual commuting variety is Gorenstein with rational singularities and its canonical module is free of rank 1.

Mots clés: polynomial algebra; complex; commuting variety; desingularization; Gorenstein; Cohen-Macaulay; rational singularities; cohomology

Domaines: Théorie des représentations [math.RT]; Géométrie algébrique [math.AG]

Jean-Yves Charbonnel, Mouchira Zaiter. ON THE GENERALIZED COMMUTING VARIETIES OF A REDUCTIVE LIE ALGEBRA. 2015. ⟨hal-01186953⟩