We study moduli spaces of sheaves over nonprojective K3 surfaces. More precisely, let omega be a Kahler class on a K3 surface S, let rgeq 2 be an integer, and let v = (r,\xi, a) be a Mukai vector on S. We show that if the moduli space M of omega-stable vector bundles with associated Mukai vector v is compact, then M is an irreducible holomorphic symplectic manifold which is deformation equivalent to a Hilbert scheme of points on a K3 surface. Moreover, we show that there is a Hodge isometry between v^{perp} and H^2(M,mathbb{Z}) and that M is projective if and only if S is projective.

Moduli spaces of bundles over nonprojective K3 surfaces

Perego, Arvid;
2017-01-01

Abstract

We study moduli spaces of sheaves over nonprojective K3 surfaces. More precisely, let omega be a Kahler class on a K3 surface S, let rgeq 2 be an integer, and let v = (r,\xi, a) be a Mukai vector on S. We show that if the moduli space M of omega-stable vector bundles with associated Mukai vector v is compact, then M is an irreducible holomorphic symplectic manifold which is deformation equivalent to a Hilbert scheme of points on a K3 surface. Moreover, we show that there is a Hodge isometry between v^{perp} and H^2(M,mathbb{Z}) and that M is projective if and only if S is projective.
File in questo prodotto:
File Dimensione Formato  
Moduli spaces of bundles over nonprojective K3 surfaces - arxiv version.pdf

accesso aperto

Descrizione: Articolo principale
Tipologia: Documento in Pre-print
Dimensione 421.12 kB
Formato Adobe PDF
421.12 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11567/897031
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 7
  • ???jsp.display-item.citation.isi??? 7
social impact