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{c}
{wiki=Hodge_theory#Hodge_decomposition}

For a compact Kähler manifold,
$$
H^k_{dR}(X;\mathbb C)=\bigoplus_{p+q=k}H^{p,q}_{\bar\partial}(X),
$$
and every class has a unique harmonic representative of each type.


Hodge decomposition theorem for compact Kähler manifolds

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 118 / 2 / c / Solution

Hodge decomposition theorem for compact Kähler manifolds

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Hodge decomposition theorem for compact Kähler manifolds

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