On rational homology projective planes with quotient singularities of small indices

TL;DR

This paper investigates the existence and classification of rational homology complex projective planes with quotient singularities of small indices, focusing on topological and smooth obstructions and their effects.

Contribution

It provides a classification of quotient singularities on rational homology projective planes with indices up to three, considering topological and smooth obstructions.

Findings

Classified quotient singularities with indices up to three

Identified topological and smooth obstructions affecting existence

Characterized smooth loci with trivial first integral homology

Abstract

In this article, we study the effects of topological and smooth obstructions on the existence of rational homology complex projective planes that admit quotient singularities of small indices. In particular, we provide a classification of the types of quotient singularities that can be realized on rational homology complex projective planes with indices up to three, whose smooth loci have trivial first integral homology group.