The moduli space of \((3,3,3)\) trilinear forms
type: Item
instance of: scholarly article
title: The moduli space of \((3,3,3)\) trilinear forms
zbMATH Open document ID: 0864.11020
DOI: 10.1007/BF02567808
author: Kok Onn Ng
published in: Manuscripta Mathematica
publication date: 1996-06-05T00:00:00Z
full work available at URL: https://eudml.org/doc/156113
review text: In a previous paper [The classification of (3,3,3) trilinear forms, J. Reine Angew. Math. 468, 49-75 (1995; Zbl 0858.11023)], we described the set of \(G\)-orbits of smooth cuboids and derived explicit matrix representations for singular cuboids. In this paper, we use the matrix representations of singular cuboids to investigate the relations among the orbits. Let \(U,V\) and \(W\) be three dimensional vector spaces over \(\mathbb{C}\) (or an algebraically closed field with characteristic not equal to 2 or 3). We prove that the moduli space of trilinear forms on \(U^* \otimes V^* \otimes W^*\) is isomorphic to \(\mathbb{P}^2\) by applying geometric invariant theory to the action of \(PGL(U) \times PGL(V) \times PGL(W)\) on \(\mathbb{P} (U\otimes V \otimes W)\).
Mathematics Subject Classification ID: 11E76
Mathematics Subject Classification ID: 14J30
Mathematics Subject Classification ID: 14L24
Mathematics Subject Classification ID: 14D20
Mathematics Subject Classification ID: 14N05
zbMATH DE Number: 866153
zbMATH Keywords: matrix representations of singular cuboids
zbMATH Keywords: orbits
zbMATH Keywords: moduli space of trilinear forms
zbMATH Keywords: geometric invariant theory
MaRDI profile type: Publication
cites work: Q4264383
cites work: Topological conditions for smoothing algebraic singularities
cites work: Q4740026
cites work: Q5652790
cites work: Lectures on introduction to moduli problems and orbit spaces
cites work: Q3710637
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description: scientific article; zbMATH DE number 866153