 K3 period domain

On the K3 intersection lattice, this open quadric has complex dimension twenty and records the period line $H^{2,0}$. Fixing a positive class $h$ of type $(1,1)$ adds $q(h,\omega )=0$ and yields a nineteen-dimensional domain for primitive polarized cohomology of signature $(2,19)$. The distinction is necessary: the unrestricted full lattice has signature $(3,19)$ and does not satisfy polarization positivity on all of $H^{1,1}$.