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

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

2003-03-25

arxiv.org/abs/math/0303308v1

Mathematics

Algebraic Geometry

22 pages, Latex 2e, submitted preprint

Scientific paper

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 $X$.

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