  Let $M$ be a hyperkahler manifold, $\Gamma$ its mapping class group, and
$Teich$ the Teichmuller space of complex structures of hyperkahler type. After
we glue together birationally equivalent points, we obtain the so-called
birational Teichmuller space $Teich_b$. Every connected component of $Teich_b$
is identified with its period space $P$ by global Torelli theorem. The mapping
class group of $M$ acts on $P$ as a finite index subgroup of the group of
isometries of the integer cohomology lattice, that is, satisfies assumptions of
Ratner theorem. We prove that there are three classes of orbits, closed, dense
and the intermediate class which corresponds to varieties with $Re(H^{2,0}(M))$
containing a given rational vector. The closure of the later orbits is a fixed
point set of an anticomplex involution of $P$. This fixes an error in the paper
1306.1498, where this third class of orbits was overlooked. We explain how this
affects the works based on 1306.1498.
