Corollary 4.20 . [00S9]

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Corollary 4.20.

(global Skoda estimate) Consider any $\varphi\in PSH(X_{s},s^{-1}\omega_{FS})$ normalised to $\sup_{X_{s}}\varphi=0$ . There are uniform positive constants $\alpha$ , $C$ , such that

\mathchoice{{\vbox{\hbox{$\textstyle-$ }}\kern-7.83337pt}}{{\vbox{\hbox{$\scriptstyle-$ }}\kern-6.11674pt}}{{\vbox{\hbox{$\scriptscriptstyle-$ }}\kern-5.48965pt}}{{\vbox{\hbox{$\scriptscriptstyle-$ }}\kern-5.31259pt}}\!\int_{X_{s}}e^{-\alpha\varphi}d\mu_{s}\leq C.

(27)