Irregular and singular loci of commuting varieties

Details Irregular and singular loci of commuting varieties Irregular and singular loci of commuting varieties

2008-01-20

arxiv.org/abs/0801.3074v2

Transformation Groups, Vol. 13 (2008), Nos. 3--4, 819--837.

Mathematics

Algebraic Geometry

15 pages Several minor corrections are implemented

Scientific paper

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.

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