  An open question is whether the Hilbert scheme of points of a high
dimensional affine space satisfies Murphy's Law, as formulated by Vakil. In
this short note, we instead consider the loci in the Hilbert scheme
parametrizing punctual schemes with a given Hilbert function, and we show that
these loci satisfy Murphy's Law. We also prove a related result for equivariant
deformations of curve singularities with $\mathbb G_m$-action.
