Mathematical Research Letters

Volume 3 (1996)

Number 6

Algebraic structures on hyperkähler manifolds

Pages: 763 – 767

DOI: http://dx.doi.org/10.4310/MRL.1996.v3.n6.a4

Author

Misha Verbitsky (Institute for Advanced Study)

Abstract

Let $M$ be a compact hyperkähler manifold. The hyperkähler structure equips $M$ with a set $\cal R$ of complex structures parametrized by $\Bbb C P^1$, called {\em the set of induced complex structures.} It was known previously that induced complex structures are {\it non-algebraic}, except maybe a countable set. We prove that a {\it countable} set of induced complex structures is {\it algebraic}, and this set is dense in $\cal R$. A more general version of this theorem was proven by A. Fujiki.

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