Birational stability of the cotangent bundle

TL;DR

This paper introduces a birational stability concept for cotangent sheaves on complex projective manifolds and orbifolds, proving their stability unless the orbifold is uniruled, based on conjectures in birational classification.

Contribution

It defines a birational stability notion for cotangent sheaves and proves their stability in most cases, advancing understanding in birational geometry.

Findings

Cotangent sheaves are birationally stable unless the orbifold is uniruled.

The work relies on standard conjectures in birational classification.

Provides a new perspective on stability in complex geometry.

Abstract

We define a birational version of the stability of cotangent sheaves for complex projective manifolds, and more generally for smooth orbifolds. We then show, using standard conjectures in birational classification, that these cotangent sheaves are birationally stable, unless the orbifold is uniruled.