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We study the higher dimensional geometry of Berkovich spaces using open fiber disks, which are given by open disks in a relative dimension $1$ fibration. Inspired by birational geometry, we conjecture that the Berkovich skeleton is the complement of the union of all open fiber disks, and prove this conjecture for X admitting a strictly semistable model with semiample canonical class.
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Brown et al. (2024) studied this question.
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