New characterizations of plurisubharmonic functions and positivity of direct image sheaves

TL;DR

This paper introduces new characterizations of plurisubharmonic functions and Griffiths positivity for holomorphic vector bundles with singular Finsler metrics, offering alternative proofs for key positivity properties in complex geometry.

Contribution

It provides novel characterizations and methods to establish plurisubharmonic variation and Griffiths positivity in complex geometric contexts.

Findings

New characterizations of plurisubharmonic functions.

Alternative proof techniques for positivity of direct image sheaves.

Enhanced understanding of Finsler metrics in complex geometry.

Abstract

We give new characterizations of plurisubharmonic functions and Griffiths positivity of holomorphic vector bundles with singular Finsler metrics. As applications, we present a different method to prove plurisubharmonic variation of generalized Bergman kernel metrics and Griffiths positivity of the direct images of twisted relative canonical bundles associated to holomorphic families of K\"ahler manifolds.