Abstract
Let
M
be a compact hyperkaehler manifold. The hyperkaehler 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 Fujiki.