Equidistribution and convergence speed for zeros of holomorphic sections of singular Hermitian line bundles

TL;DR

This paper proves that zeros of random holomorphic sections of powers of a semipositive singular Hermitian line bundle become evenly distributed, providing explicit estimates on how quickly this convergence occurs.

Contribution

It introduces new results on the equidistribution and convergence speed of zeros for sections of singular Hermitian line bundles, extending previous work to singular settings.

Findings

Zeros of random sections are equidistributed in the limit.

Explicit convergence speed estimates are provided.

Results apply to semipositive singular Hermitian line bundles.

Abstract

We establish the equidistribution of zeros of random holomorphic sections of powers of a semipositive singular Hermitian line bundle, with an estimate of the convergence speed.