L'application cotangente des surfaces de type general

TL;DR

This paper investigates surfaces of general type with globally generated cotangent sheaves, introducing a cotangent map to analyze obstructions to ampleness, classifying surfaces with many non-ample curves.

Contribution

It defines the cotangent map for surfaces of general type and classifies surfaces with infinitely many non-ample curves, advancing understanding of cotangent sheaf ampleness.

Findings

Classification of surfaces with infinite non-ample curves

Partial classification of non-ample curves

Introduction of the cotangent map as an analytical tool

Abstract

We study surfaces of general type $S$ whose cotangent sheaf is generated by its global sections. We define a map called the cotangent map of $S$ that enables us to understand the obstructions to the ampleness of the cotangent sheaf of $S$. These obstructions are curves on $S$ that we call "non-ample". We classify surfaces with an infinite number of non-ample curves and we partly classify the non-ample curves.