A resolution of the Sylvester-Gallai problem of J.-P. Serre
type: Item
instance of: scholarly article
title: A resolution of the Sylvester-Gallai problem of J.-P. Serre
zbMATH Open document ID: 0593.51002
DOI: 10.1007/BF02187687
published in: Discrete \& Computational Geometry
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/186383
review text: The author calls a point set a Sylvester-Gallai configuration (SGC) if every line joining two points of the set contains at least one member of the set. Gallai proved that a SGC in the real plane is confined to a line; this can be generalized to ordered projective or affine spaces. The author shows using results of Hirzebruch that a SGC in complex space is confined to a plane (Theorem). A further statement needed is the following: If a SGC of a pappian affine plane is a subset of 3 concurrent lines but not of one line, then the associated field has nonzero characteristic (Lemma 2).
Mathematics Subject Classification ID: 51A20
Mathematics Subject Classification ID: 51A45
Mathematics Subject Classification ID: 51G05
zbMATH DE Number: 3953686
zbMATH Keywords: Sylvester-Gallai configuration
Wikidata QID: Q56454689
author: Leroy M. Kelly
reviewed by: Hermann Heineken
MaRDI profile type: Publication
cites work: Q3735854
cites work: Q3043303
cites work: Recent results in complex differential geometry
cites work: On the Chern numbers of surfaces of general type
cites work: The Lines and Planes Connecting the Points of a Finite Set
cites work: Semi-stable curves on algebraic surfaces and logarithmic pluricanonical maps
cites work: Calabi's conjecture and some new results in algebraic geometry
DBLP publication ID: journals/dcg/Kelly86
description: scientific article; zbMATH DE number 3953686