Equation 5.2.10C44E7362B437

\begin{equation} \mathrm d^{\mathrm c}=\frac{\mathrm{i}}{4\pi }(\bar\partial -\partial )=\frac{\partial -\bar\partial }{4\pi \mathrm{i}}, \qquad \text{so that}\qquad \mathrm d\mathrm d^{\mathrm c}=\frac{\mathrm{i}}{2\pi }\partial \bar\partial =\mathrm{dd}^{\mathrm{c}}. \end{equation}