Irregular and singular loci of commuting varieties
Algebraic Geometry
2009-10-05 v2 Group Theory
Representation Theory
Abstract
We prove that the singular locus of the commuting variety of a noncommutative reductive Lie algebra is contained in the irregular locus and we compute the codimension of the latter. We prove that one of the irreducible components of the irregular locus has codimension 4. This yields the lower bound of the codimension of the singular locus, in particular, implies that it is at least 2. We also prove that the commuting variety is rational.
Cite
@article{arxiv.0801.3074,
title = {Irregular and singular loci of commuting varieties},
author = {Vladimir L. Popov},
journal= {arXiv preprint arXiv:0801.3074},
year = {2009}
}
Comments
15 pages Several minor corrections are implemented