The moduli space of \(\mathbb Q\)-homology projective planes with 5 quotient singular points
type: Item
instance of: scholarly article
title: The moduli space of \(\mathbb Q\)-homology projective planes with 5 quotient singular points
zbMATH Open document ID: 1192.14031
published in: Acta Mathematica Vietnamica
publication date: 2010-06-18T00:00:00Z
full work available at URL: Toc ACTA 1 35.htm
review text: A normal complex projective surface \(S\) is called a \(\mathbb Q\)-homology projective plane it it has the same Betti numbers as \(\mathbb P^2\). If \(S\) is smooth then \(S\) is either isomorphic to \(\mathbb P^2\) or a so-called fake projective plane. It follows from the Bogomolov-Miyaoka-Yau inequality then if \(S\) has quotient singularities then there are at most five singular points. The author proves that if \(S\) has five quotient singularities then there are three \(A_1\)-singularities and two \(A_3\)-singularities. Moreover, the minimal resolution of singularities \(S'\) of \(S\) is an Enriques surface. The author shows that the moduli space of Enriques surfaces obtained in this way is zero-dimensional.
reviewed by: Remke Kloosterman
Mathematics Subject Classification ID: 14J17
Mathematics Subject Classification ID: 14J28
zbMATH DE Number: 5723516
zbMATH Keywords: \(\mathbb Q\)-homology projective planes
zbMATH Keywords: Enriques surfaces
author: Jonghae Keum
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5723516