On the Commuting variety of a reductive Lie algebra and other related varieties.
Résumé
In this note, we discuss some varieties which are constructed analogously to the
isospectral commuting varieties. These varieties are subvarieties of varieties having
very simple desingularizations. For instance, this is the case of the nullcone of
any cartesian power of a reductive Lie algebra and we prove that it is normal. Moreover,
as a byproduct of these investigations and a Ginzburg's result, we get that the
normalizations of the isospectral commuting variety and the commuting variety have
rational singularities.
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