Convergence of Bergman measures towards the Zhang measure

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.

29 pages

References in corpus (2)

• Equidistribution of Weierstrass points on curves over non-Archimedean fields
• Topology of Hybrid Analytifications