Complete intersections on general hypersurfaces
  We ask when certain complete intersections of codimension $r$ can lie on a generic hypersurface in $\PP^n$. We give a complete answer to this question when $2r \leq n+2$ in terms of the degrees of the hypersurfaces and of the degrees of the generators of the complete intersection. 
E.Carlini, L.Chiantini and A.V.Geramita