Let $X$ be a compact Kähler manifold. For every integer $k\ge 0$, identify
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\begin{align*}
H^k(X,\mathbb Q)\otimes_{\mathbb Q}\mathbb C
\end{align*}
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with $H^k(X,\mathbb C)$ by the canonical extension of scalars map. Then there are complex subspaces $H^{p,q}(X)\subset H^k(X,\mathbb C)$, indexed by pairs $p,q\ge 0$ with $p+q=k$, such that