Let $X$ be a complex manifold of complex dimension $n$, and let $A^{p,q}(X)$ denote the space of smooth complex-valued differential forms of type $(p,q)$ on $X$. Then the [exterior derivative](/theorems/1525) on complex-valued forms decomposes uniquely as
paragraph
admin
\begin{align*}
d = \partial + \bar{\partial},
\end{align*}