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

Markus Zowislok

ISBN 10: 3838119088 / ISBN 13: 9783838119083

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

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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.

Codice articolo 9783838119083

Dati bibliografici

• Titolo: On Moduli Spaces of Semistable Sheaves on K3 Surfaces : In Search of new Irreducible Symplectic Manifolds
• Editore: Südwestdeutscher Verlag Für Hochschulschriften AG Co. KG
• Data di pubblicazione: 2010
• Lingua: Inglese
• ISBN 10: 3838119088
• ISBN 13: 9783838119083
• Rilegatura: Taschenbuch
• Condizione: Neu
• Dimensioni: 220 L x 150 A x 8 P (millimetri) 220 millimetri di larghezza per 150 millimetri di altezza per 8 millimetri di profondità
• Peso: 197 grammi

Descrizione articolo

Riassunto

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.

L'autore

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.