Equation 6.17.29F558292FE56

\begin{equation} \begin{aligned} \mathrm{dd}^{\mathrm{c}}\log S={}& \frac{\mathrm i}{2\pi S^2} \sum _{j<l}\mathrm e^{w_ j+w_ l} (\chi _ j\alpha _ l-\chi _ l\alpha _ j) \wedge \overline{(\chi _ j\alpha _ l-\chi _ l\alpha _ j)}\\ & +\frac{\sum _ j\chi _ j^2\mathrm e^{w_ j}\mathrm{dd}^{\mathrm{c}}w_ j}{S} +2\frac{\sum _ j\mathrm e^{w_ j} \bigl (\chi _ j\mathrm{dd}^{\mathrm{c}}\chi _ j-\frac{\mathrm i}{2\pi } \partial \chi _ j\wedge \bar\partial \chi _ j\bigr )}{S}, \end{aligned} \end{equation}