Algebraic structures on hyperkaehler manifold

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Let M be a compact hyperkaehler manifold. The hyperkaehler structure equips M with a set R of complex structures parametrized by CP¹, 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 Fujiki.