Conic sections in space defined by intersection conditions
type: Item
instance of: scholarly article
title: Conic sections in space defined by intersection conditions
zbMATH Open document ID: 1090.51007
author: Hans-Peter Schröcker
published in: Beiträge zur Algebra und Geometrie
publication date: 2005-10-20T00:00:00Z
full work available at URL: https://eudml.org/doc/126145
full work available at URL: 1.html
review text: The author continues the study of the set \(S_m\), \(0\leq m\leq 3\), of planes in the projective three-space that intersect \(m\) conic sections and \(6-2m\) straight lines in six points of a conic. The paper under review deals with the cases \(m=2, 3\). (See Beitr. Algebra Geom. 46, No. 2, 435--446 (2005; Zbl 1090.51008) for \(m=0\) and J. Geom. Graph. 8, 59--68 (2004; Zbl 1081.51501) for \(m=1\).) By using a unified method, it is shown that for all \(S_m\), \(0\leq m\leq 3\), the solution manifold is in general algebraic, of class \(8-m\). The algebraic equation for \(S_m\) in the homogeneous plane coordinates is derived from a non-algebraic equation for a supermanifold. Special lines and planes in \(S_m\) are also determined.
reviewed by: Mihai Cipu
Mathematics Subject Classification ID: 51N15
Mathematics Subject Classification ID: 51N35
Mathematics Subject Classification ID: 14N10
zbMATH DE Number: 2216468
zbMATH Keywords: incidence
zbMATH Keywords: conic section
zbMATH Keywords: pencil of planes
zbMATH Keywords: star product
MaRDI profile type: Publication
description: scientific article