Nilpotent commuting varieties of reductive Lie algebras
arXiv:math/0302204 · doi:10.1007/s00222-003-0315-6
Abstract
We prove that the nilpotent commuting variety of a reductive Lie algebra over an algebraically closed field of good characteristic is equidimensional. In characteristic zero, this confirms a conjecture of Vladimir Baranovsky. As a by-product, we obtain tat the punctual (local) Hilbert scheme parametrising the ideals of colength $n$ in $k[[X,Y]]$ is irreducible over any algebraically closed field $k$.
25 pages