Schichten von Matrizen sind rationale Varietäten. (Sheets of matrices are rational varieties)
type: Item
instance of: scholarly article
title: Schichten von Matrizen sind rationale Varietäten. (Sheets of matrices are rational varieties)
zbMATH Open document ID: 0641.14015
DOI: 10.1007/BF01457501
author: Klaus Bongartz
published in: Mathematische Annalen
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164493
review text: We prove that the sheets of \(gl_ n\) are rational varieties. Furthermore, generalizing the well-known concept of the companion-matrix of a polynomial, we construct affine subspaces of \(gl_ n\) which are transversal cross-sections. Our construction is somewhat easier to understand than Petersons cross-sections. Moreover, all our results and proofs are true also in positive characteristic.
Mathematics Subject Classification ID: 14M20
Mathematics Subject Classification ID: 14L35
Mathematics Subject Classification ID: 20G15
zbMATH DE Number: 4043995
zbMATH Keywords: sheets of matrices
zbMATH Keywords: transversal cross-sections
zbMATH Keywords: positive characteristic
zbMATH Keywords: elementary divisor
MaRDI profile type: Publication
cites work: Über Schichten halbeinfacher Lie-Algebren
cites work: Über Bahnen und deren Deformationen bei linearen Aktionen reduktiver Gruppen
cites work: Parametrisierung von Konjugationsklassen in \(\mathfrak sl_n\)
description: scientific article; zbMATH DE number 4043995