  We represent algebraic curves via commuting matrix polynomials. This allows
us to show that the Hilbert scheme of cohomologically stable twisted rational
curves of degree $d$ in ${\Bbb P}^3\backslash {\Bbb P}^1$ is isomorphic to a
complexified hyperk\"ahler quotient of an open subset of a vector space by a
non-reductive Lie group.
