Moduli of Gorenstein Q-homology projective planes

TL;DR

This paper classifies all complex Q-homology projective planes with certain singularities and trivial canonical bundle, describing their moduli spaces explicitly as rational curves over Q.

Contribution

It provides a complete classification of these surfaces, detailing their one-dimensional moduli spaces and explicit constructions via elliptic surfaces and involutions.

Findings

31 types of such surfaces identified

All moduli are rational curves over Q

Explicit families constructed using elliptic surfaces

Abstract

We give a complete classification of complex Q-homology projective planes with isolated rational double point singularities and numerically trivial canonical bundle. There are 31 types, and each has one-dimensional moduli. In fact, all moduli curves are rational and defined over Q, and we determine all families explicitly using extremal rational elliptic surfaces and Enriques involutions of base change type.