A non-vanishing conjecture for cotangent bundles on elliptic surfaces

TL;DR

This paper proves the non-vanishing conjecture for cotangent bundles on isotrivial elliptic surfaces, resolving a key question for surfaces with Kodaira dimension at most 1.

Contribution

It establishes the non-vanishing conjecture for cotangent bundles on a broad class of elliptic surfaces, completing the picture for low Kodaira dimension cases.

Findings

Proves the non-vanishing conjecture for isotrivial elliptic surfaces.

Completes the classification for surfaces with Kodaira dimension ≤ 1.

Builds on and extends results by Höring and Peternell.

Abstract

In this paper, we prove the non-vanishing conjecture for cotangent bundles on isotrivial elliptic surfaces. Combined with the result by H\"{o}ring and Peternell, it completely solves the question for surfaces with Kodaira dimension at most $1$.