On the group of automorphisms of Horikawa surfaces

Minimal algebraic surfaces of general type X such that K X 2 =2χ(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 ,χ) such that K 2 =2χ-6, every irreducible component of Gieseker's moduli space 𝔐 K 2 ,χ contains an open subset consisting of surfaces with group of automorphisms isomorphic to ℤ 2 .