Differential form of type (p, q) (source code)

= Differential form of type (p, q)
{title2=$\Omega^{p,q}(X)$}

The complexified cotangent bundle of a <complex manifold> splits as
$$
T^*X\otimes\mathbb C=(T^{1,0}X)^*\oplus(T^{0,1}X)^*.
$$
A differential form has type $(p,q)$ when it is locally a sum of terms containing $p$ factors $dz^j$ and $q$ factors $d\bar z^k$.

= (p, q)-form
{synonym}