= Holomorphic p-form on a complex manifold
{title2=$\alpha\in H^0(X,\Omega_X^p)$}
A <differential form of type (p, q)> of type $(p,0)$ is <holomorphic> when its local coefficients in <holomorphic coordinates> are <holomorphic functions>, equivalently $\bar\partial\alpha=0$. It need not be $d$-closed on every <complex manifold>. Top-degree <holomorphic> forms are closed by bidegree. On a <compact> <complex surface>, <holomorphic> forms of all degrees are closed, even without a <Kähler metric>.
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