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

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.

14 pages, 1 figure. To appear in Rendiconti del Seminario Matematico di Torino