Bott-Chern Poincaré lemma
= Bott-Chern Poincaré lemma
{c}
On a <polydisc>, $H_{BC}^{p,q}=0$ for $p,q>0$. A <Poincare lemma> primitive for a closed pure-type form can be modified by exact terms until only bidegrees $(p-1,q)$ and $(p,q-1)$ remain. The <Dolbeault-Poincaré lemma> and <conjugate Dolbeault-Poincaré lemma> then make the original form $\partial\bar\partial$-exact.