Compact dual of a period domain
= Compact dual of a period domain
{title2=$\check D$}
The compact dual is the complex projective flag variety imposing prescribed filtration dimensions and $Q(F^p,F^{w-p+1})=0$, but neither real opposition nor positivity. In weight one it is the complex <Lagrangian Grassmannian>. In polarized K3 weight two it is an isotropic-line quadric.