Canonical rings of Gorenstein stable Godeaux surfaces

TL;DR

This paper extends the understanding of canonical rings to Gorenstein stable Godeaux surfaces, proving that those with torsion of order at least 3 are smoothable, thus broadening the classification of these surfaces.

Contribution

It introduces a new result showing the smoothability of Gorenstein stable Godeaux surfaces with certain torsion properties, expanding previous descriptions of their canonical rings.

Findings

Gorenstein stable Godeaux surfaces with torsion ≥ 3 are smoothable

Extension of canonical ring descriptions from prior work

Broader classification of Gorenstein stable Godeaux surfaces

Abstract

Extending the description of canonical rings from \cite{reid78} we show that every Gorenstein stable Godeaux surface with torsion of order at least $3$ is smoothable.