Singular Q-homology planes of negative Kodaira dimension have smooth locus of non-general type

TL;DR

This paper proves that Q-homology planes with negative Kodaira dimension have smooth loci that are not of general type, extending previous results to a broader class of surfaces.

Contribution

It establishes a new classification result for Q-homology planes with negative Kodaira dimension, generalizing earlier work on contractible surfaces.

Findings

Smooth locus of such planes is not of general type

Extends Koras-Russell's result to a wider class of surfaces

Advances the classification of Q-acyclic surfaces

Abstract

We continue the program of classification of normal Q-acyclic surfaces defined over the field of complex numbers, so-called 'Q-homology planes'. Here we show that if a Q-homology plane has negative Kodaira dimension then its smooth locus is not of general type. This generalizes an earlier result of Koras-Russell for contractible surfaces.