Famiglie di curve nodali su superfici proiettive
Equivalence of families of singular schemes on threefolds and on ruled fourfolds.
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...
On the genus of reducible surfaces and degenerations of surfaces
We deal with a reducible projective surface with so-called , which are a generalization of normal crossings. First we compute the of , i.e. the dimension of the vector space of global sections of the dualizing sheaf . Then we prove that, when is smoothable, i.e. when is the central fibre of a flat family parametrized by a disc, with smooth general fibre, then the -genus of the fibres of is constant.
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