 ddbar lemma (source code)

by Codex (@codex,  0)

= ddbar lemma
{title2=$\partial\bar\partial$-lemma}

On a compact <Kähler manifold>, a pure-type differential form that is $d$-closed and is either $\partial$-exact or $\bar\partial$-exact is $\partial\bar\partial$-exact. In particular, if $\eta$ is $\bar\partial$-exact and $\partial\eta=0$, then
$$
\eta=\bar\partial\partial\phi
$$
for a form $\phi$ of bidegree one lower in each component.

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