A description of the Brauer-Severi scheme of trace rings of generic matrices
type: Item
instance of: scholarly article
title: A description of the Brauer-Severi scheme of trace rings of generic matrices
zbMATH Open document ID: 0884.16015
author: George F. Seelinger
published in: Journal of Algebra
publication date: 1997-12-09T00:00:00Z
review text: Let \(k\) be an algebraically closed field of characteristic 0, and let \(T\) denote the trace ring of \(m\) generic \(n\times n\) matrices over \(k\). The paper under review gives a description of the Brauer-Severi scheme for \(T\) (i.e., for the fibers of \(T\)). It is shown that the Brauer-Severi scheme for \(T\) is isomorphic to \(\text{Proj}(Q)\) for an appropriate (and described with its generators) graded ring \(Q\). Another important contribution in this paper is the study of the local properties of \(T\) considered as a sheaf over \(\text{Spec}(C)\) where \(C\) is the centre of \(T\). Sufficient conditions are found for the Brauer-Severi scheme of the fiber of \(T\) having smooth irreducible components that meet transversally. In addition, the case \(m=n=2\) is dealt with as an important example. The paper contains new interesting results; it is organized in an appropriate way, and provides sources for further research.
Mathematics Subject Classification ID: 16R30
Mathematics Subject Classification ID: 14F22
Mathematics Subject Classification ID: 16S60
zbMATH DE Number: 941270
zbMATH Keywords: Brauer-Severi schemes
zbMATH Keywords: generic matrices
zbMATH Keywords: matrix invariants
zbMATH Keywords: trace rings
zbMATH Keywords: associated graded rings
zbMATH Keywords: sheaves
zbMATH Keywords: fibers
reviewed by: Plamen Koshlukov
MaRDI profile type: Publication
full work available at URL: jabr.1996.0288
OpenAlex ID: W2011637857
DOI: 10.1006/JABR.1996.0288
description: scientific article; zbMATH DE number 941270