Automorphisms of a family of surfaces with $p_g=q=2$ and $K^2=7$

TL;DR

This paper determines the automorphism groups of a specific family of complex surfaces with particular invariants, providing insights relevant to the Mumford-Tate conjecture.

Contribution

It explicitly computes the automorphism groups for all surfaces in a family with given invariants, extending understanding of their symmetries.

Findings

Automorphism groups are fully characterized for the family.

Results have implications for the Mumford-Tate conjecture.

Provides new examples of surfaces with computed automorphisms.

Abstract

We compute the automorphism group of all the elements of a family of surfaces of general type with $p_g=q=2$ and $K^2=7$, originally constructed by C. Rito. We discuss the consequences of our results towards the Mumford-Tate conjecture.