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

TL;DR

This paper classifies automorphism groups of certain minimal surfaces of general type, establishing bounds on their size and prime factors, advancing understanding of their symmetries.

Contribution

It provides a complete classification of automorphism groups for minimal surfaces with specific invariants and bounds their order and prime factors.

Findings

Automorphism group order is at most 200.

Prime factors of automorphism groups are limited to primes ≤ 31, excluding 29.

Classification of automorphism groups for the given surfaces.

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 $p \neq 29$.