On metrics with minimal singularities of line bundles whose stable base loci admit holomorphic tubular neighborhoods

TL;DR

This paper characterizes the minimal singularities of metrics on big line bundles over projective manifolds with stable base loci that have holomorphic tubular neighborhoods, extending understanding of line bundle metrics in complex geometry.

Contribution

It provides an explicit description of minimal singularities of metrics on line bundles with stable base loci admitting holomorphic tubular neighborhoods, especially for non-semi-ample nef and big line bundles.

Findings

Explicit description of minimal singularities under certain normal bundle conditions

Application to higher-dimensional analogues of Zariski's example

Insights into metrics on non-semi-ample nef and big line bundles

Abstract

We investigate the minimal singularities of metrics on a big line bundle $L$ over a projective manifold when the stable base locus $Y$ of $L$ is a submanifold of codimension $r\geq 1$. Under some assumptions on the normal bundle and a neighborhood of $Y$, we give a explicit description of the minimal singularity of metrics on $L$. We apply this result to study a higher (co-)dimensional analogue of Zariski's example, in which the line bundle $L$ is not semi-ample, however it is nef and big.