  The Hessian of a general cubic surface is a nodal quartic surface, hence its
desingularisation is a K3 surface. We determine the transcendental lattice of
the Hessian K3 surface for various cubic surfaces (with nodes and/or Eckardt
points for example). Classical invariant theory shows that the moduli space of
cubic surfaces is a weighted projective space. We describe the singular locus
and some other subvarieties of the moduli space.
