 Primitive cohomology (source code)

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= Primitive cohomology
{title2=$P^k=\ker([\kappa]^{d-k+1}:H^k\to H^{2d-k+2})$}

For a compact <Kähler manifold> of complex dimension $d$ and $k\le d$, this is the cohomology killed by the indicated power of a <Kähler class>. The Hodge–Riemann bilinear relations polarize its <Hodge structure>. On a <K3 surface>, primitive degree-two cohomology is the orthogonal complement of the chosen positive class.

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