Canonical rings of Gorenstein stable Godeaux surfaces

Abstract

Extending the description of canonical rings from Reid (J Fac Sci Univ Tokyo Sect IA Math 25(1):75–92, 1978) we show that every Gorenstein stable Godeaux surface with torsion of order at least 3 is smoothable

Smoothing semi-smooth Stable Godeaux surfaces

“…Our starting point is the systematic analysis of a part of the boundary of the moduli of stable Godeaux surfaces carried out in [FPR18a], where all the non-canonical Gorenstein stable Godeaux surfaces have been classified explicitly. The question whether these surfaces actually belong to the closure of the moduli space of smooth Godeaux surfaces is partially answered in [FPR18a] and [FR18], [Ro16], but the smoothability of some of the non-normal examples is still to be decided.…”