Equation 20.2.353C4F71AC116E

\begin{equation} \begin{aligned} \operatorname{vol}_{X|Y}(\alpha ) & = \lim _{\epsilon \to 0+}\int _ Y \Bigl (\theta |_ Y + \epsilon \omega |_ Y + \mathrm{dd}^{\mathrm{c}}V_{\theta + \epsilon \omega }|_ Y\Bigr )^ m\\ =& \lim _{\epsilon \to 0+}\int _ Y \left(\theta |_ Y + \epsilon \omega |_ Y + \mathrm{dd}^{\mathrm{c}}\operatorname{Tr}_ Y^{\theta + \epsilon \omega }(V_{\theta + \epsilon \omega }) \right)^ m \\ & =\int _ Y \left( \theta |_ Y+\mathrm{dd}^{\mathrm{c}}\operatorname{Tr}_ Y^{\theta }(V_{\theta }) \right)^ m, \end{aligned} \end{equation}