The classification of isotrivially fibred surfaces with p_g=q=2

TL;DR

This paper classifies isotrivially fibred surfaces with geometric genus and irregularity equal to 2, extending previous results and providing new examples of minimal surfaces of general type with specific invariants.

Contribution

It completes and extends the classification of such surfaces, offering new examples of minimal surfaces with particular invariants.

Findings

Classification of isotrivially fibred surfaces with p_g=q=2

New examples of minimal surfaces with K^2=4,5,6

Extension of Zucconi's previous results

Abstract

An isotrivially fibred surface is a smooth projective surface endowed with a morphism onto a curve such that all the smooth fibres are isomorphic to each other. The first goal of this paper is to classify the isotrivially fibred surfaces with $p_g=q=2$ completing and extending a result of Zucconi. As an important byproduct, we provide new examples of minimal surfaces of general type with $p_g=q=2$ and $K^2=4,5$ and a first example with $K^2=6$.