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

Flaminio Flamini

Collectanea Mathematica (2004)

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

Abstract

top
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

top

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 -

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.