  A projective hypersurface is nodal if it does not have singularities worse
than simple nodes. We calculate the rational cohomology of the spaces of
equations of nodal cubic and quartic plane curves and also nodal cubic surfaces
in the projective 3-space. We deduce the cohomology of the corresponding spaces
of equations and moduli spaces. In the case of plane cubics we use the method
of conical resolutions. We handle plane quartics by applying a more general
version of this method which we construct in this paper. For cubic surfaces we
use an explicit description of the compact GIT quotient.
