Gorenstein $\mathbb{Q}$-homology projective planes

TL;DR

This paper provides a comprehensive classification of all possible singularity types on Gorenstein -homology projective planes, identifying 58 types with explicit examples for most.

Contribution

It offers the complete list of singularity types on Gorenstein -homology projective planes, filling a gap in the classification of these algebraic surfaces.

Findings

58 possible singularity types identified

All but two types have explicit examples

Complete classification of singularities on these surfaces

Abstract

We present the complete list of all singularity types on Gorenstein $\mathbb{Q}$-homology projective planes, i.e., normal projective surfaces of second Betti number one with at worst rational double points. The list consists of $58$ possible singularity types, each except two types supported by an example.