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Definition 18.15.6F217B40D9074

Definition 18.15.6.F217B40D9074 For a normalized ordinary model $q$ in background $\eta $ on $C$, put

\[ \Phi (q)=\Psi +q\circ p,\qquad \mathcal S_\Psi =\{ \Phi (q):P_\eta [q]=q\} . \]

Write $\mu _ q=\mathbf1_{\{ q=-\infty \} }(\eta +\mathrm{dd}^{\mathrm{c}}q)$ for the polar curvature of $q$, and define

7DFF38FB6056 18.15.7
\begin{equation} \rho _\Psi (\Phi (q_1),\Phi (q_2)) =\| \mu _{q_1}-\mu _{q_2}\| _{\mathrm{TV}}. \end{equation}
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