Automorphisms of Minimal Surfaces of General Type with $K_S^2 = 1$, $p_g = 2$

Abstract

We classify the automorphism group of minimal surfaces of general type with $K_S^2 = 1$ and $\rho_g = 2$. Furthermore, we show that the order of the automorphism group is bounded above by 200 and can only have prime factors $p \leq 31$ with $p \neq 29$.