 Polarized Hodge structure

A polarization is a nondegenerate integral bilinear form of symmetry $(-1{)}^w$, orthogonal on Hodge summands except complementary bidegrees, satisfying the displayed positivity for every nonzero $v\in H^{p,q}$. This convention takes the cup-product pairing as the primitive geometric polarization. Omitting the constant sign factor and rescaling $Q$ is an equivalent convention. The full intersection pairing of a K3 surface is not itself a polarization: its real $(1,1)$ space has one positive direction as well as nineteen negative directions.