We study moduli spaces of sheaves over nonprojective K3 surfaces. More precisely, let be a Kähler class on a K3 surface , let be an integer, and let be a Mukai vector on . We show that if the moduli space of -stable vector bundles with associated Mukai vector is compact, then 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 and and that is projective if and only if is projective.
"Moduli spaces of bundles over nonprojective K3 surfaces." Kyoto J. Math. 57 (1) 107 - 146, April 2017. https://doi.org/10.1215/21562261-3759540