Complex conjugation of differential-form type
= Complex conjugation of differential-form type
<Complex conjugate>[Complex conjugation] interchanges the bidegrees of complex differential forms:
$$
\overline{\Omega^{p,q}(X)}=\Omega^{q,p}(X).
$$
It also interchanges the two type components of the <exterior derivative>, so $\bar\partial\bar\alpha=\overline{\partial\alpha}$ and $\partial\bar\alpha=\overline{\bar\partial\alpha}$.