  We construct a new twenty-dimensional family of projective eight-dimensional
irreducible holomorphic symplectic manifolds: the compactified moduli space
M_3(Y) of twisted cubics on a smooth cubic fourfold Y that does not contain a
plane is shown to be smooth and to admit a contraction M_3(Y) -> Z(Y) to a
projective eight-dimensional symplectic manifold Z(Y). The construction is
based on results on linear determinantal representations of singular cubic
surfaces.
