  The main purpose of this paper is twofold. We first want to analyze in
details the meaningful geometric aspect of the method introduced in the
previous paper [12], concerning regularity of families of irreducible, nodal
"curves" on a smooth, projective threefold $X$. This analysis highlights
several fascinating connections with families of other singular geometric
"objects" related to $X$ and to other varieties.
  Then, we generalize this method to study similar problems for families of
singular divisors on ruled fourfolds suitably related to $X$.
