English

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.

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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