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Algebraic structures on hyperkaehler manifold

Misha Verbitsky
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Abstract

Let $M$ be a compact hyperkaehler manifold. The hyperkaehler structure equips $M$ with a set $R$ of complex structures parametrized by $CP^1$, 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 Fujiki.

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Misha Verbitsky. 1996-10-10. Algebraic structures on hyperkaehler manifold. https://arxiv.org/abs/alg-geom/9609011

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