On the Commuting variety of a reductive Lie algebra.

Jean-Yves Charbonnel (1)

1 IMJ - Institut de Mathématiques de Jussieu

The commuting variety of a reductive Lie algebra ${\goth g}$ is the underlying variety of a well defined subscheme of $\gg g{}$. In this note, it is proved that this scheme has rational singularities. In particular, its ideal of definition is a prime ideal.

Mots clés: polynomial algebra; complex; commuting variety; Cohen-Macaulay; homology; projective dimension; depth

Domaines: Théorie des représentations [math.RT]; Géométrie algébrique [math.AG]

Jean-Yves Charbonnel. On the Commuting variety of a reductive Lie algebra.. 2012. ⟨hal-00711467v1⟩