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

Flaminio Flamini
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Abstract

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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Flaminio Flamini. 2003-03-25. Equivalence of families of singular schemes on threefolds and on ruled fourfolds. https://arxiv.org/abs/math/0303308

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