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

Markus Zowislok

ISBN 10: 3838119088 / ISBN 13: 9783838119083

Verlag: Südwestdeutscher Verlag Für Hochschulschriften AG Co. KG, 2010

Beschreibung

nach der Bestellung gedruckt Neuware - Printed after ordering - 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.v8 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.

Bestandsnummer des Verkäufers 9783838119083

Bibliografische Details

• Titel: On Moduli Spaces of Semistable Sheaves on K3 Surfaces : In Search of new Irreducible Symplectic Manifolds
• Verlag: Südwestdeutscher Verlag Für Hochschulschriften AG Co. KG
• Erscheinungsjahr: 2010
• Sprache: Englisch
• ISBN-10: 3838119088
• ISBN-13: 9783838119083
• Einband: Taschenbuch
• Zustand: Neu
• Abmessungen: 220B x 150 H x 8 T Millimeter Breite: 220 mm, Höhe: 150 mm, Tiefe: 8 mm
• Gewicht: 197 Gramm

Über diesen Titel

Inhaltsangabe

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.

Über die Autorin bzw. den Autor

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