Moduli spaces of bundles over non-projective K3 surfaces

Arvid Perego (1) , Matei Toma (1)

1 IECL - Institut Élie Cartan de Lorraine

We study moduli spaces of sheaves over non-projective K3 surfaces. More precisely, if v = (r, ξ, a) is a Mukai vector on a K3 surface S with r prime to ξ and ω is a " generic " Kähler class on S, we show that the moduli space M of µ ω −stable sheaves on S with associated Mukai vector v is an irreducible holo-morphic symplectic manifold which is deformation equivalent to a Hilbert scheme of points on a K3 surface. If M parametrizes only locally free sheaves, it is moreover hyperkähler. Finally, we show that there is an isometry between v ⊥ and H 2 (M, Z) and that M is projective if and only if S is projective.

Mots clés: moduli spaces of sheaves; twisted sheaves; K3 surfaces

Domaines: Géométrie algébrique [math.AG]; Variables complexes [math.CV]

Arvid Perego, Matei Toma. Moduli spaces of bundles over non-projective K3 surfaces. 2016. ⟨hal-01269780⟩