Proposition 4.8 . [0167]

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Proposition 4.8.

The map $\rho^{\mathrm{hyb}}$ is continuous and surjective. Further, we have

\operatorname{Log}_{\mathcal{X}}\circ\rho^{\mathrm{hyb}}=r_{{\mathcal{X}}{\mathcal{X}}^{\prime}}\circ\operatorname{Log}_{{\mathcal{X}}^{\prime}}+O((\log|t|)^{-1})

(4.2)

on $X_{{\mathbb{D}}^{*}_{r}}$ for $0<r\ll 1$ .