Gorenstein log del Pezzo surfaces. II
type: Item
instance of: scholarly article
title: Gorenstein log del Pezzo surfaces. II
zbMATH Open document ID: 0801.14013
author: M. Miyanishi
author: De-Qi Zhang
published in: Journal of Algebra
publication date: 1994-02-07T00:00:00Z
review text: [For part I see the authors, J. Algebra 118, No. 1, 63-84 (1988; Zbl 0664.14019)] A projective normal surface \(\overline V\) is a Gorenstein log Del Pezzo surface if it has only rational double singularities and the canonical divisor is ample. In the paper under review, the fundamental group of the smooth part of such a surface is determined. Main result: Let \(f : V \to \overline V\) be a minimal resolution and let \(D : = f^{-1} (\text{Sing} (\overline V))\), where \(\text{Sing}(\overline V)\) is the singular locus. Let \(V^ 0 : = \overline V -\text{Sing} (\overline V)\). Then the fundamental group \(\pi_ 1 (V^ 0)\) of the smooth part \(V^ 0\) is an abelian group of order \(\leq 9\). In the paper are also classified Gorenstein log Del Pezzo surfaces, \(\overline V\), under the assumption that \(\overline V\) is relatively minimal. Existence results are also given.
reviewed by: Mauro C. Beltrametti
Mathematics Subject Classification ID: 14J25
Mathematics Subject Classification ID: 14F35
Mathematics Subject Classification ID: 14M05
Mathematics Subject Classification ID: 14E20
zbMATH DE Number: 495544
zbMATH Keywords: quasi-universal covering
zbMATH Keywords: abelian fundamental group
zbMATH Keywords: projective normal surface
zbMATH Keywords: fundamental group
MaRDI profile type: Publication
full work available at URL: jabr.1993.1069
OpenAlex ID: W2036410765
DOI: 10.1006/JABR.1993.1069
description: scientific article; zbMATH DE number 495544