Ramified cover of varieties with nef cotangent bundle

TL;DR

This paper constructs examples demonstrating that nef cotangent bundles are not preserved under ramified covers and that manifolds with Stein universal covers may lack nef cotangent bundles, challenging existing conjectures.

Contribution

It provides the first known examples showing nef cotangent bundles are not stable under ramified covers and refutes a conjecture relating Stein universal covers to nef cotangent bundles.

Findings

Nef cotangent bundle not preserved under finite ramified covers

Manifolds with Stein universal cover may not have nef cotangent bundle

Disproves Liu-Maxim-Wang conjecture

Abstract

We construct examples to show that having nef cotangent bundle is not preserved under finite ramified covers. Our examples also show that a projective manifold with Stein universal cover may not have nef cotangent bundle, disproving a conjecture of Liu-Maxim-Wang.