Algebraic Structures on Hyperkk Ahler Manifolds Algebraic Structures on Hyperkk Ahler Manifolds

Let M be a compact hyperkk ahler manifold. The hy-perkk ahler structure equips M with a set R of complex structures parametrized by C P 1 , called the set of induced complex structures. It was known previously that induced complex structures are non-algebraic, except may be a countable set. We prove that a countable set of induced complex structures is algebraic, and this set is dense in R. A more general version of this theorem was proven by A. Fujiki. The structure of this paper is following. In Subsection 1.1 we deene hyperkk ahler manifolds and induced complex structures. In Subsection 1.2, we deene induced complex structures of general type. The main result of this paper and its proof are given in Section 2.