Markus Zowislok (Mainz)

Abstract. Up to now only very few examples of irreducible holomorphically symplectic manifolds are known, and all of them arise from moduli spaces of sheaves on projective K3 or abelian surfaces that are semistable with respect to an ample divisor.
For a general ample divisor the question whether one can construct holomorphically symplectic manifolds is completely solved.
Restricting to K3 surfaces, we extend these results to the case of Mukai vector (0,c,0), where there is no notion of a general ample divisor, and to many cases of a nongeneral ample divisor, including all cases of sheaves of dimension 1 and those of rank 2.