On Moduli Spaces of Semistable Sheaves on K3 Surfaces: In Search of new Irreducible Symplectic Manifolds - Couverture souple

Zowislok, Markus

 
9783838119083: On Moduli Spaces of Semistable Sheaves on K3 Surfaces: In Search of new Irreducible Symplectic Manifolds
Couverture souple
ISBN 10 : 3838119088 ISBN 13 : 9783838119083
Editeur : Südwestdeutscher Verlag für Hochschulschriften, 2010

Synopsis

A big challenge in symplectic geometry is the search for irreducible symplectic manifolds. After O'Grady constructed striking examples out of singular moduli spaces of sheaves on projective abelian and K3 surfaces for special nonprimitive Mukai vectors v with v.v=8, Kaledin, Lehn and Sorger proved that for all nonprimitive Mukai vectors v with v.v>8 the moduli space is not symplectically resolvable if the ample divisor is general. In this thesis we investigate the remaining cases of moduli spaces of semistable sheaves on projective K3 surfaces - the cases of Mukai vector (0,c,0) as well as moduli spaces for nongeneral ample divisors - with regard to the possible construction of new examples of projective irreducible symplectic manifolds. We establish a connection to the already investigated moduli spaces or generalisations thereof, and we are able to extend the known results to all of the open remaining cases for rank 0 and many of those for positive rank. In particular, we can exclude for these cases the existence of new examples of projective irreducible symplectic manifolds lying birationally over components of the moduli space.

Les informations fournies dans la section « Synopsis » peuvent faire référence à une autre édition de ce titre.

Présentation de l'éditeur

A big challenge in symplectic geometry is the search for irreducible symplectic manifolds. After O'Grady constructed striking examples out of singular moduli spaces of sheaves on projective abelian and K3 surfaces for special nonprimitive Mukai vectors v with v.v=8, Kaledin, Lehn and Sorger proved that for all nonprimitive Mukai vectors v with v.v>8 the moduli space is not symplectically resolvable if the ample divisor is general. In this thesis we investigate the remaining cases of moduli spaces of semistable sheaves on projective K3 surfaces - the cases of Mukai vector (0,c,0) as well as moduli spaces for nongeneral ample divisors - with regard to the possible construction of new examples of projective irreducible symplectic manifolds. We establish a connection to the already investigated moduli spaces or generalisations thereof, and we are able to extend the known results to all of the open remaining cases for rank 0 and many of those for positive rank. In particular, we can exclude for these cases the existence of new examples of projective irreducible symplectic manifolds lying birationally over components of the moduli space.

Biographie de l'auteur

Markus Zowislok, born 1980 in Germany, has studied physics and mathematics in Cologne and Helsinki. In 2006 he moved to Mainz, where he worked as a research associate at the institute for mathematics until 2010.

Les informations fournies dans la section « A propos du livre » peuvent faire référence à une autre édition de ce titre.

Éditeur
Südwestdeutscher Verlag für Hochschulschriften
Date d'édition
2010
Langue
anglais
ISBN 10 
3838119088
ISBN 13 
9783838119083
Reliure
Broché
Nombre de pages
120
Coordonnées du fabricant
non disponible
Personne responsable
non disponible