Ergänzung ''Über rationale Darstellungen von Kettengeometrien als projektive Varietäten''. (Complement to ''On rational representations of chain geometries as projective varieties'')
type: Item
instance of: scholarly article
title: Ergänzung ''Über rationale Darstellungen von Kettengeometrien als projektive Varietäten''. (Complement to ''On rational representations of chain geometries as projective varieties'')
zbMATH Open document ID: 0601.51009
DOI: 10.1007/BF01190366
author: Armin Herzer
published in: Archiv der Mathematik
publication date: 1987-01-01T00:00:00Z
review text: In his paper in Geom. Dedicata 19, 287-293 (1985; Zbl 0573.51002) the author gave a very general construction for ''rational representations of chain geometries'' for a finite-dimensional K-algebra \({\mathfrak R}\), where the point set is a quasiprojective variety and the chains are smooth rational curves on it all of the same order r. In this construction a Grassmann map is followed by an appropriate projection. Here the author proves the following theorem: Let \({\mathfrak V}\) be the point set in a rational representation of the chain geometry \(\Sigma\) (K,\({\mathfrak R})\). Then \({\mathfrak V}\) is a projective variety if and only if \({\mathfrak R}\) is semisimple.
Mathematics Subject Classification ID: 51B99
Mathematics Subject Classification ID: 51N35
zbMATH DE Number: 3969509
zbMATH Keywords: rational representations of chain geometries
zbMATH Keywords: projective variety
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/bf01190366
OpenAlex ID: W1979208398
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description: scientific article; zbMATH DE number 3969509