= Polarized Hodge structure
{title2=$(-1)^{w(w-1)/2}i^{p-q}Q(v,\bar v)>0$}
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.
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