Dolbeault-Poincaré lemma
= Dolbeault-Poincaré lemma
{c}
On a sufficiently small polydisc in a <complex manifold>, every $\bar\partial$-closed $(p,q)$-form with $q>0$ is locally $\bar\partial$-exact. A coefficientwise one-variable integral operator and induction over the coordinates prove the result.