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

Collectanea Mathematica (2004)

• Volume: 55, Issue: 1, page 37-60
• ISSN: 0010-0757

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## Abstract

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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.

## How to cite

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Flamini, Flaminio. "Equivalence of families of singular schemes on threefolds and on ruled fourfolds.." Collectanea Mathematica 55.1 (2004): 37-60. <http://eudml.org/doc/44328>.

@article{Flamini2004,
abstract = {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.},
author = {Flamini, Flaminio},
journal = {Collectanea Mathematica},
keywords = {Curvas; 3-variedades; Haces; threefold; nodal curve; vector bundle; Severi variety},
language = {eng},
number = {1},
pages = {37-60},
title = {Equivalence of families of singular schemes on threefolds and on ruled fourfolds.},
url = {http://eudml.org/doc/44328},
volume = {55},
year = {2004},
}

TY - JOUR
AU - Flamini, Flaminio
TI - Equivalence of families of singular schemes on threefolds and on ruled fourfolds.
JO - Collectanea Mathematica
PY - 2004
VL - 55
IS - 1
SP - 37
EP - 60
AB - 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.
LA - eng
KW - Curvas; 3-variedades; Haces; threefold; nodal curve; vector bundle; Severi variety
UR - http://eudml.org/doc/44328
ER -

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