The main purpose of this paper is twofold. We first analyze in detail the meaningful geometric aspect of the method introduced in [12], concerning families of irreducible, nodal curves on a smooth, projective threefold X. This analysis gives some geometric interpretations not investigated in [12] and highlights several interesting connections with families of other singular geometric objects related to X and to other varieties. Then we use this method to study analogous problems for families of singular divisors on ruled fourfolds suitably related to X. This enables us to show that Severi varieties of vector bundles on X can be rephrased in terms of classical Severi varieties of divisors on such fourfolds.
@article{urn:eudml:doc:44328,
title = {Equivalence of families of singular schemes on threefolds and on ruled fourfolds.},
journal = {Collectanea Mathematica},
volume = {55},
year = {2004},
pages = {37-60},
zbl = {1077.14050},
mrnumber = {MR2028980},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44328}
}
Flamini, Flaminio. Equivalence of families of singular schemes on threefolds and on ruled fourfolds.. Collectanea Mathematica, Tome 55 (2004) pp. 37-60. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44328/