Equation 10.24.14349718BCBE33

\begin{gather} \pi ^*\phi _0=\sum _ jm_ j\log |\sigma _ j|^2+\ell _0,\qquad \pi ^*(\omega +\mathrm{dd}^{\mathrm{c}}\phi _0)=\sum _ jm_ j[D_ j]+R_0, \\ K_ Y=\pi ^*K_ X+\sum _ jb_ jD_ j,\qquad \pi ^*\mathrm{d}V_ X=\prod _ j|\sigma _ j|^{2b_ j}\mathrm{d}V_ Y. \tag{10.24.15} \end{gather}