Resolutions of surfaces with big cotangent bundle and $A_2$ singularities

TL;DR

This paper establishes new criteria for when surface resolutions have big cotangent bundles and provides lower bounds for degrees of hypersurfaces in projective space with this property.

Contribution

It introduces a novel criterion for big cotangent bundles on resolved surfaces and determines new degree bounds for hypersurfaces deformation equivalent to such surfaces.

Findings

New criterion for big cotangent bundles on surface resolutions

Lower bounds for degrees of hypersurfaces with big cotangent bundles

Identification of deformation equivalence conditions

Abstract

We give a new criterion for when a resolution of a surface of general type with canonical singularities has big cotangent bundle and a new lower bound for the values of $d$ for which there is a surface with big cotangent bundle that is deformation equivalent to a smooth hypersurface in $\mathbb{P}^3$ of degree $d$.