A characterization of finite vector bundles on Gauduchon astheno-Kahler manifolds

TL;DR

This paper extends the characterization of finite vector bundles, originally established for projective varieties, to compact complex manifolds with Gauduchon astheno-Kahler metrics, broadening the understanding of their structure.

Contribution

It generalizes Nori's theorem to a wider class of complex manifolds, showing the equivalence of finiteness and triviality after finite etale Galois coverings in this setting.

Findings

Finite vector bundles on Gauduchon astheno-Kahler manifolds are characterized similarly to projective varieties.

The pullback of a finite bundle to a finite etale Galois cover is trivial.

The theorem confirms the equivalence between finiteness and triviality after covering in this broader context.

Abstract

A vector bundle E on a projective variety X is called finite if it satisfies a nontrivial polynomial equation with integral coefficients. A theorem of Nori implies that E is finite if and only if the pullback of E to some finite etale Galois covering of X is trivial. We prove the same statement when X is a compact complex manifold admitting a Gauduchon astheno-Kahler metric.