= Hodge–Riemann bilinear relations
{c}
{title2=$(-1)^{k(k-1)/2}i^{p-q}\int_X v\wedge\bar v\wedge\kappa^{d-k}>0$}
For a nonzero primitive class $v\in H^{p,q}$ of degree $k=p+q$ on a compact <Kähler manifold> of complex dimension $d$, the displayed expression is positive. Together with orthogonality of complementary Hodge bidegrees, this makes primitive cohomology a <polarized Hodge structure> when the <Kähler class> is rational, after clearing denominators. Positivity on the full cohomology requires the signs prescribed by its primitive decomposition.
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