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

Flaminio Flamini

Ayuda

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

Autores: Flaminio Flamini
Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 55, Fasc. 1, 2004, págs. 37-60
Idioma: inglés
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Resumen
- 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 showthat Severi varieties of vector bundles on $X$ can be rephrased in terms of “classical” Severi varieties of divisors on such fourfolds.
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