Pluri-cotangent maps of surfaces of general type

TL;DR

This paper investigates the properties of pluri-cotangent maps on complex surfaces of general type with strongly semi-ample cotangent bundles, exploring their geometric and algebraic structures.

Contribution

It provides a detailed study of the morphisms induced by global sections of symmetric powers of the cotangent bundle on such surfaces.

Findings

Analysis of the structure of pluri-cotangent maps

Conditions for the maps to be embeddings or finite

Implications for the geometry of surfaces of general type

Abstract

Let $X$ be a compact, complex surface of general type whose cotangent bundle $\Omega_X$ is strongly semi-ample. We study the pluri-cotangent maps of $X$, namely the morphisms $\psi_n \colon \mathbb{P}(\Omega_X) \to \mathbb{P}(H^0(X, \, S^n \Omega_X))$ defined by the vector space of global sections $H^0(X, \, S^n \Omega_X)$.