On an asymptotic characterisation of Griffiths semipositivity

TL;DR

This paper establishes an equivalence between Griffiths semipositivity of certain Hermitian metrics and an asymptotic extension property, providing a new characterization that resolves a question posed by Deng, Ning, Wang, and Zhou.

Contribution

It introduces an asymptotic extension property as a criterion for Griffiths semipositivity, offering a novel characterization for possibly non-smooth Hermitian metrics.

Findings

Hermitian metrics are Griffiths-semipositively curved if and only if they satisfy the asymptotic extension property

The result applies to possibly non-smooth metrics

Answers a previously open question by Deng, Ning, Wang, and Zhou

Abstract

We prove that certain possibly non-smooth Hermitian metrics are Griffiths-semipositively curved if and only if they satisfy an asymptotic extension property. This result answers a question of Deng--Ning--Wang--Zhou in the affirmative.