On equidistribution theorem for multi-sequences of holomorphic line bundles

TL;DR

This paper investigates the distribution of zeros of random holomorphic sections across multiple sequences of line bundles and examines the growth of dimensions in pseudo-effective line bundles, advancing understanding in complex geometry.

Contribution

It introduces new results on the equidistribution of zeros for multi-sequences of holomorphic line bundles and analyzes dimension growth in pseudo-effective line bundles.

Findings

Zeros of random sections are equidistributed with respect to singular measures.

Dimension growth rates are characterized for pseudo-effective line bundles.

Provides new insights into the asymptotic behavior of holomorphic line bundle sequences.

Abstract

Given several sequences of Hermitian holomorphic line bundles $\{(L_{kp}, h_{kp})\}_{p=1}^{\infty}$, we establish the distribution of common zeros of random holomorphic sections of $L_{kp}$ with respect to singular measures. We also study the dimension growth for a sequence of pseudo-effective line bundles.