Convergence of Bergman measures towards the Zhang measure
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math.AG
math.DG
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measurebergmanconvergenceberkovichspacezhangalongamini
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We prove a folklore conjecture that the Bergman measure along a holomorphic family of curves parametrized by the punctured unit disk converges to the Zhang measure on the associated Berkovich space. The convergence takes place on a Berkovich hybrid space. We also study the convergence of the Bergman measure to a measure on a metrized curve complex in the sense of Amini and Baker.
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