Let $M$ be a complex manifold of complex dimension $n$. For integers $p,q$, let $\Omega^{p,q}(M)$ denote the complex [vector space](/page/Vector%20Space) of smooth complex differential forms of type $(p,q)$ on $M$, with $\Omega^{p,q}(M)=\{0\}$ when $p<0$, $q<0$, $p>n$, or $q>n$. Let
Under the natural identification $\Lambda^{0,0}T^*M\cong M\times\mathbb C$ and hence $\Omega^{0,0}(M)=C^\infty(M;\mathbb C)$, there is an equality of complex vector spaces