The geography of irregular surfaces

TL;DR

This paper reviews the distribution of key numerical invariants of irregular complex surfaces of general type, providing insights into their geometric properties and recent developments in the field.

Contribution

It offers an overview of results on irregular complex surfaces, focusing on the distribution of invariants like self-intersection of the canonical divisor and Euler characteristic.

Findings

Distribution patterns of invariants analyzed

Connections between invariants and surface geometry discussed

Updated overview of recent research presented

Abstract

We give an overview of results on irregular complex surfaces of general type, discussing in particular the distribution of the numerical invariants self-intersection of a canonical divisor and holomorphic Euler characteristic for the minimal ones. This is an expanded version of the talk given by the second author at the workshop "Classical Algebraic Geometry Today", M.S.R.I., January 26--30, 2009.