  Minimal algebraic surfaces of general type $X$ such that
$K^2_X=2\chi(\mathcal{O}_X)-6$ are called Horikawa surfaces. In this note the
group of automorphisms of Horikawa surfaces is studied. The main result states
that given an admissible pair $(K^2, \chi)$ such that $K^2=2\chi-6$, every
connected component of Gieseker's moduli space $\mathfrak{M}_{K^2,\chi}$
contains an open subset consisting of surfaces with group of automorphisms
isomorphic to $\mathbb{Z}_2$.

Algebraic Geometry