Notes on automorphisms of surfaces of general type with $p_g=0$ and $K^2=7$

Abstract

Let $S$ be a smooth minimal complex surface of general type with $p_g=0$ and $K^2=7$. We prove that any involution on $S$ is in the center of the automorphism group of $S$. As an application, we show that the automorphism group of an Inoue surface with $K^2=7$ is isomorphic to ${\mathbb{Z}}_2^2$ or ${\mathbb{Z}}_2\times {\mathbb{Z}}_4$. We construct a $2$-dimensional family of Inoue surfaces with automorphism groups isomorphic to ${\mathbb{Z}}_2\times {\mathbb{Z}}_4$.

14 pages, 2 figures

References in corpus (1)

• Automorphisms of numerical Godeaux surfaces with torsion of order 3, 4, or 5