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arXiv · 2005.05753

Convergence of Bergman measures towards the Zhang measure

Sanal Shivaprasad
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Abstract

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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Sanal Shivaprasad. 2020-05-12. Convergence of Bergman measures towards the Zhang measure. https://arxiv.org/abs/2005.05753

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