On the generalized commuting varieties of a reductive Lie algebra
Representation Theory
2015-08-26 v1 Algebraic Geometry
Abstract
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.
Keywords
Cite
@article{arxiv.1508.06174,
title = {On the generalized commuting varieties of a reductive Lie algebra},
author = {Jean-Yves Charbonnel and Mouchira Zaiter},
journal= {arXiv preprint arXiv:1508.06174},
year = {2015}
}
Comments
arXiv admin note: substantial text overlap with arXiv:1204.0377, arXiv:1507.05419