= Dolbeault resolution of holomorphic differential forms
{c}
{title2=$0\to\Omega^p\to\mathcal A^{p,0}\xrightarrow{\bar\partial}\mathcal A^{p,1}\to\cdots$}
The <Dolbeault-Poincaré lemma> makes this a locally exact complex of <sheaves>, with degree-zero kernel the <holomorphic differential forms>. The <sheaves> of smooth forms are <fine sheaves> by a <partition of unity>. The <acyclic resolution theorem> therefore computes the cohomology of $\Omega^p$ by the global <Dolbeault operator> complex.
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