Let G be a connected reductive algebraic group over an algebraically closed field k of characteristic p ≥ 0, and g = Lie G. In positive characteristic, suppose in addition that p is good for G and the derived subgroup of G is simply connected. LetN = N (g) denote the nilpotent variety of g, and C(g) := {(x, y) ∈ N × N | [x, y] = 0}, the nilpotent commuting variety of g. Our main goal in this paper is to show that the variety C(g) is equidimensional. In characteristic 0, this confirms a… CONTINUE READING