  Let (G, V) be a representation with either G a torus or (G, V) a locally free
stable $\theta$-representation. We study the fiber at 0 of the associated
moment map, which is a commuting variety in the latter case. We characterize
the cases where this fiber is normal. The quotient (i.e. the symplectic
reduction) turns out to be a specific orbifold when the representation is
polar. In the torus case, this confirms a conjecture stated by C. Lehn, M.
Lehn, R. Terpereau and the author in a former article. In the $\theta$-case,
the conjecture was already known but the present approach yield another proof.
