Helly-type theorems for varieties
type: Item
instance of: scholarly article
title: Helly-type theorems for varieties
zbMATH Open document ID: 0679.14002
DOI: 10.1016/S0195-6698(89)80058-7
published in: European Journal of Combinatorics
publication date: 1989-01-01T00:00:00Z
review text: Let \(\Gamma\) be a commutative field and let \(\Gamma [X_ 0,...,X_ n]\) be the ring of all homogeneous polynomials in \(n+1\) variables over \(\Gamma\). Main theorem: Let \(d\geq 1\) and let V be a d-dimensional vector subspace of \(\Gamma [X_ 0,...,X_ n]\). Then V has the (d-1)-Helly property. Moreover, if \(\Gamma\) is infinite, then V does not have the (d-2)-Helly property.
Mathematics Subject Classification ID: 14A10
Mathematics Subject Classification ID: 14A05
Mathematics Subject Classification ID: 12E05
Mathematics Subject Classification ID: 54D20
zbMATH DE Number: 4112742
zbMATH Keywords: intersection of spheres
zbMATH Keywords: Helly property
author: Peter Frankl
MaRDI profile type: Publication
cites work: A Helly type theorem for hypersurfaces
cites work: Q4133994
cites work: Helly-type theorems for spheres
description: scientific article; zbMATH DE number 4112742