Cohomological rank functions and surfaces of general type with $p_g=q=2$

TL;DR

This paper classifies minimal surfaces of general type with geometric genus and irregularity both equal to 2, focusing on those with specific invariants, providing a detailed understanding of their structure.

Contribution

It introduces a classification of minimal surfaces with p_g=q=2 and specific invariants K_S^2=5 or 6, expanding the understanding of surfaces of general type.

Findings

Classification of surfaces with p_g=q=2 and K_S^2=5 or 6

Identification of new geometric properties of these surfaces

Detailed description of their moduli spaces

Abstract

We classify minimal surfaces $S$ with $p_g=q=2$ and $K_S^2=5$ or $6$.