Canonical surfaces with big cotangent bundle

TL;DR

This paper introduces a new criterion for surfaces of general type with canonical singularities to have a minimal resolution with a big cotangent bundle, expanding the class of known examples with negative second Segre number.

Contribution

It provides a novel criterion linking canonical singularities to big cotangent bundles on minimal resolutions, broadening the understanding of such surfaces.

Findings

Many new examples of surfaces with negative second Segre number and big cotangent bundle.

A criterion ensuring big cotangent bundle for surfaces with canonical singularities.

Extension of known classes of surfaces with positive second Segre number.

Abstract

Surfaces of general type with positive second Segre number are known to have big cotangent bundle. We give a new criterion ensuring that a surface of general type with canonical singularities has a minimal resolution with big cotangent bundle. This provides many examples of surfaces with negative second Segre number and big cotangent bundle.