  We prove, among other things, that the Specht ideal of a two-rowed partition
is perfect over an arbitrary field, provided that the characteristic is either
zero or large enough with respect to certain numerical parameters of the ideal.
In particular we give a self-contained proof of Cohen-Macaulayness of the
so-called $h$-equals set, a result previously obtained by Etingof-Gorsky-Losev
over the complex numbers using rational Cherednik algebras.
