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

2016/12/24 by Genki Hosono, Hosono, Genki, Takayuki Koike +1
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.1612.08212

openalex publication_date 2016/12/24 · openalex created_date 2018/11/29 · openalex updated_date 2026/07/28

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≥ 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.

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