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Comptes Rendus Mathématique
Volume 348, n° 9-10
pages 565-569 (mai 2010)
Doi : 10.1016/j.crma.2010.03.015
Received : 27 October 2009 ;  accepted : 23 Mars 2010
Stable pairs on elliptic K3 surfaces
Couples stables sur une surface K3 elliptique
 

Marcello Bernardara
Universität Duisburg-Essen, Fakultät für Mathematik, Universitätsstr. 2, 45117 Essen, Germany 

Abstract

We study semistable pairs on elliptic K3 surfaces with a section: we construct a family of moduli spaces of pairs, related by wall crossing phenomena, which can be studied to describe the birational correspondence between moduli spaces of sheaves of rank 2 and Hilbert schemes on the surface. In the 4-dimensional case, this can be used to get the isomorphism between the moduli space and the Hilbert scheme described by Friedman.

The full text of this article is available in PDF format.
Résumé

On considère sur une surface K3 elliptique avec une section une notion de stabilité pour un couple. On obtient une famille d’espaces de modules reliés par wall crossing, dont l’étude permet de décrire les correspondances birationnelles entre les espaces de modules des faisceaux stables de rang 2 et les schémas de Hilbert sur la surface. En particulier, en dimension 4, ceci permet de décrire l’isomorphisme entre l’espace des module et le schéma de Hilbert demontré par Friedman.

The full text of this article is available in PDF format.


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