Automorphisms of order three on numerical Godeaux surfaces

TL;DR

This paper proves that numerical Godeaux surfaces cannot possess automorphisms of order three, clarifying the symmetry constraints of these complex algebraic surfaces.

Contribution

It establishes a non-existence result for automorphisms of order three on numerical Godeaux surfaces, a previously unresolved question.

Findings

Numerical Godeaux surfaces do not admit automorphisms of order three.

The proof rules out the presence of such automorphisms.

This result constrains the symmetry properties of these surfaces.

Abstract

We prove that a numerical Godeaux surface cannot have an automorphism of order three.