On the diophantine equation \(1=\sum \frac{1}{n_ i}+\frac{1}{\prod n_ i}\quad and\) a class of homologically trivial complex surface singularities
type: Item
instance of: scholarly article
title: On the diophantine equation \(1=\sum \frac{1}{n_ i}+\frac{1}{\prod n_ i}\quad and\) a class of homologically trivial complex surface singularities
zbMATH Open document ID: 0616.14032
author: Yanyan Li
published in: Pacific Journal of Mathematics
publication date: 1988-01-01T00:00:00Z
review text: In this paper we investigate the relation between an elementary problem in the theory of unit (or Egyptian) fractions, and the local topological structure of isolated singularities of complex surfaces, namely: Let \(n_ 1,...,n_ N\) be integers \(\geq 2\), and let \(x\in X\) be an isolated two-dimensional complex singularity whose dual intersection graph is a star with central \(weight\quad 1\) and with \(weights\quad n\) on the arms. Then X is locally the cone on a homology 3-sphere if and only if \(\sum n_ i^{-1}+(\prod n_ i)^{-1}=1.\quad All\) such unit fraction expressions for 1 are given for \(N\leq 7\), and properties of such sequences \(\{n_ i\}\) are discussed in general.
Mathematics Subject Classification ID: 14J17
Mathematics Subject Classification ID: 32S05
Mathematics Subject Classification ID: 11D61
zbMATH DE Number: 3997987
zbMATH Keywords: Egyptian fraction
zbMATH Keywords: topological structure of isolated singularities of complex surfaces
Wikidata QID: Q29028469
MaRDI profile type: Publication
full work available at URL: pjm.1988.133.41
OpenAlex ID: W1979468280
DOI: 10.2140/PJM.1988.133.41
description: scientific article; zbMATH DE number 3997987