A homology plane of general type can have at most a cyclic quotient singularity

TL;DR

This paper proves that a homology plane of general type can have at most one cyclic quotient singularity, and demonstrates the existence of such a surface with a singular point, also analyzing automorphism groups of related surfaces.

Contribution

It establishes the maximum number of cyclic quotient singularities on homology planes of general type and characterizes automorphism groups of smooth contractible surfaces of this type.

Findings

A homology plane of general type has at most one cyclic quotient singularity.

Such a surface with a singular point does exist.

The automorphism group of a smooth contractible surface of general type is cyclic.

Abstract

We show that a homology plane of general type has at worst a single cyclic quotient singular point. An example of such a surface with a singular point does exist. We also show that the automorphism group of a smooth contractible surface of general type is cyclic.