In this article our main goal is to establish an $L^2$ version of the wisted invariance of plurigenera. We equally simplify the original "two towers" approach of Yum-Tong Siu.
"Siu’s invariance of plurigenera: a one-tower proof." J. Differential Geom. 76 (3) 485 - 493, July 2007. https://doi.org/10.4310/jdg/1180135695