On Moduli Spaces of Semistable Sheaves on K3 Surfaces

In Search of new Irreducible Symplectic Manifolds

Markus Zowislok (Autor)

Buch | Softcover

120 Seiten

2010
Südwestdeutscher Verlag für Hochschulschriften
978-3-8381-1908-3 (ISBN)

Infos

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.

Autor

Zowislok, MarkusMarkus 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.

Produkt-Details

• Erscheint lt. Verlag: 15.11.2015
• Sprache: englisch
• Gewicht: 195 g
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• Schlagworte: moduli space • nongeneral ample divisor • Symplectic variety • twisted stability
• ISBN-10: 3-8381-1908-8 / 3838119088
• ISBN-13: 978-3-8381-1908-3 / 9783838119083
• Zustand: Neuware