Linearization of transition functions of a semi-positive line bundle along a certain submanifold

2020/02/18 by Takayuki Koike, Koike, Takayuki · 2 citations
Mathematics · #14C20 #32J25 #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.2002.07830

openalex publication_date 2020/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be a complex manifold and L be a holomorphic line bundle on X. Assume that L is semi-positive, namely L admits a smooth Hermitian metric with semi-positive Chern curvature. Let Y be a compact Kähler submanifold of X such that the restriction of L to Y is topologically trivial. We investigate the obstruction for L to be unitary flat on a neighborhood of Y in X. As an application, for example, we show the existence of nef, big, and non semi-positive line bundle on a non-singular projective surface.

Cited by

• On the Non-Semipositivity of a Nef and Big Line Bundle on Grauert's Example
• Pluripotential geometry on semi-positive effective divisors of numerical dimension one

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