We consider pairs of n × n commuting matrices over an algebraically closed field F . For n, a, b (all at least 2) let V(n, a, b) be the variety of all pairs (A,B) of commuting nilpotent matrices such that AB = BA = A = B = 0. In [14] Schröer classified the irreducible components of V(n, a, b) and thus answered a question stated by Kraft [9, p. 201] (see also [3] and [10]). If μ = (μ1, μ2, . . ....