Topological Euler numbers in a semi-stable degeneration of surfaces
type: Item
instance of: scholarly article
title: Topological Euler numbers in a semi-stable degeneration of surfaces
zbMATH Open document ID: 1052.14040
published in: Proceedings of the Japan Academy. Series A
publication date: 2003-01-01T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.pja/1116443607
review text: The author proves a lower bound for the topological Euler number of surfaces in a semistable degeneration by means of Euler numbers of components and double curves in the central fibre. As an application he proves that if we have a semistable degeneration with a minimal Enriques surface as a general fibre and such that the central fibre is normal then the number of singularities of the central fibre is at most \(10\). He also gives an example showing that this upper bound can be attained.
reviewed by: Adrian Langer
Mathematics Subject Classification ID: 14J28
Mathematics Subject Classification ID: 14D06
Mathematics Subject Classification ID: 14F45
Mathematics Subject Classification ID: 14J17
zbMATH DE Number: 2024718
zbMATH Keywords: minimal Enriques surface
zbMATH Keywords: singularities
author: Yongnam Lee
MaRDI profile type: Publication
OpenAlex ID: W2086099073
cites work: The index of elliptic operators. III
cites work: Q4027240
cites work: Toroidal embeddings. I
cites work: Q4212603
cites work: Threefolds and deformations of surface singularities
cites work: DEGENERATIONS OFK3 SURFACES AND ENRIQUES SURFACES
cites work: ON MODIFICATIONS OF DEGENERATIONS OF SURFACES WITH κ=0
cites work: NUMERICAL BOUNDS FOR DEGENERATIONS OF SURFACES OF GENERAL TYPE
cites work: Q4428942
cites work: Generalisation of the Bogomolov-Miyaoka-Yau Inequality to Singular Surfaces
cites work: The maximal number of quotient singularities on surfaces with given numerical invariants
cites work: Semistable degenerations of Enriques' and hyperelliptic surfaces
cites work: On the most algebraic K3 surfaces and the most extremal log Enriques surfaces
cites work: On degenerations of algebraic surfaces
cites work: Degeneration of surfaces with trivial canonical bundle
cites work: Projective degenerations of Enriques' surfaces
cites work: Compactifications of the moduli spaces of hyperelliptic surfaces
cites work: Q4308037
DOI: 10.3792/PJAA.79.42
description: scientific article; zbMATH DE number 2024718