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The main purpose of this paper is twofold. We first \udanalyze in detail the meaningful geometric aspect of the method \udintroduced in previous papers of the author, concerning \udfamilies of irreducible, nodal "curves" on a smooth, projective threefold X.  \udThis analysis gives some geometric interpretations not investigated in the previous papers and \udhighlights several interesting connections with families of other singular geometric \ud"objects" related to X and to other varieties. \ud\udThen, we use this method to study analogous \udproblems for families of singular divisors on ruled fourfolds suitably \udrelated to X. This enables us to show that Severi varieties of vector bundles \udon X can be rephrased in terms of "classical" Severi varieties of divisors \udon such fourfolds

Equivalence of families of singular schemes on threefolds and on ruled fourfolds