Algebraic geometry of the eigenvector mapping for a free rigid body
type: Item
instance of: scholarly article
title: Algebraic geometry of the eigenvector mapping for a free rigid body
zbMATH Open document ID: 1253.14033
author: Isao Naruki
author: Daisuke Tarama
published in: Differential Geometry and its Applications
publication date: 2011-10-12T00:00:00Z
review text: This article deals with the algebro-geometric aspects of the eigenvector mapping for a dynamical system of a free rigid body on SO(3), which is governed by the Manakov equation. The authors investigate the eigenvector mapping which is regarded as a rational mapping to the complex projective plane \(P_2(\mathbb C)\) from the product of the elliptic curves, one of which is the curve given by the first integrals of the dynamical system and the other the spectral curve of the Manakov equation. The authors show that the eigenvector mapping admits a factorisation through a Kummer surface, which is a double covering of the projective plane branched along a sextic curve associated with the dynamics. It turns out that their essentials are determined by the Cremona transformation of the projective plane and some elliptic fibrations of the Kummer surface.
reviewed by: Shigeki Matsutani
Mathematics Subject Classification ID: 14H52
Mathematics Subject Classification ID: 14H70
Mathematics Subject Classification ID: 14J27
Mathematics Subject Classification ID: 14J28
Mathematics Subject Classification ID: 70E15
zbMATH DE Number: 5957585
zbMATH Keywords: Free rigid body
zbMATH Keywords: Manakov equation
zbMATH Keywords: Eigenvector mapping
zbMATH Keywords: Kummer surface
zbMATH Keywords: Cremona involution
zbMATH Keywords: Elliptic surface
Wikidata QID: Q115356883
MaRDI profile type: Publication
full work available at URL: j.difgeo.2011.04.023
OpenAlex ID: W2043283480
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DOI: 10.1016/J.DIFGEO.2011.04.023
description: scientific article; zbMATH DE number 5957585