Automorphism group schemes of bielliptic and quasi-bielliptic surfaces

Bielliptic and quasi-bielliptic surfaces form one of the four classes of minimal smooth projective surfaces of Kodaira dimension $0$. In this article, we determine the automorphism schemes of these surfaces over algebraically closed fields of arbitrary characteristic, generalizing work of Bennett and Miranda over the complex numbers; we also find some cases that are missing from the classification of automorphism groups of bielliptic surfaces in characteristic $0$.