= Dolbeault cohomology of a complex torus
{c}
{title2=$H^{p,q}_{\bar\partial}(V/\Lambda)\cong\bigwedge^pV^*\otimes\bigwedge^q\overline{V^*}$}
For a <complex torus> $X=V/\Lambda$ of complex dimension $g$, constant forms give a natural isomorphism $H^{p,q}_{\bar\partial}(X)\cong\bigwedge^pV^*\otimes\bigwedge^q\overline{V^*}$. A flat <Kähler metric> and the <Dolbeault Hodge decomposition> prove that these constant forms are precisely the harmonic representatives. Thus $h^{p,q}=\binom gp\binom gq$ for $0\leq p,q\leq g$, and zero otherwise.
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