Algebraic Montgomery-Yang problem: the non-rational surface case
type: Item
instance of: scholarly article
title: Algebraic Montgomery-Yang problem: the non-rational surface case
zbMATH Open document ID: 1273.14080
published in: Michigan Mathematical Journal
publication date: 2013-06-06T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.mmj/1363958239
review text: A \(\mathbb{Q}\)-homology plane is a normal projective surface with the same Betti numbers as the projective plane. Kollár conjectured that a \(\mathbb{Q}\)-homology plane \(S\) with quotient singularities has at most three singular points, if \(S\backslash \mathrm{Sing}(S)\) is simply connected. In the paper under review, the authors continue their study on Kollár's conjecture (see their previous paper [Math. Ann. 350, No. 3, 721--754 (2011; Zbl 1228.14033)]) and confirm this conjecture with an extra condition that \(S\) is not rational. The main ingredients of the proof are orbifold Bogomolov-Miyaoka-Yau inequalities and lattice theory.
reviewed by: Zhi Jiang
Mathematics Subject Classification ID: 14J29
Mathematics Subject Classification ID: 14J17
zbMATH DE Number: 6171213
zbMATH Keywords: rational homology plane
zbMATH Keywords: algebraic Montgomery-Yang problem
author: Dongseon Hwang
author: Jonghae Keum
MaRDI profile type: Publication
OpenAlex ID: W2032480469
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DOI: 10.1307/MMJ/1363958239
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description: scientific article; zbMATH DE number 6171213