Some elliptic fibrations arising from free rigid body dynamics
type: Item
instance of: scholarly article
title: Some elliptic fibrations arising from free rigid body dynamics
zbMATH Open document ID: 1276.14015
author: Isao Naruki
author: Daisuke Tarama
published in: Hokkaido Mathematical Journal
publication date: 2012-10-26T00:00:00Z
full work available at URL: https://projecteuclid.org/euclid.hokmj/1351086221
review text: The dynamics of free rigid body governed by the Euler equation is studied from a complex algebro-geometric viewpoint. The authors show that the dynamics is expressed by an elliptic fibration over \(\mathbb{P}^3\), which has singularities. By desingularizion and other several algebraic operations to the naive elliptic fibration, they also construct its Weierstrass normal form, which is bimeromorphic to the family of the spectral curves arising from the corresponding Manakov equation. In other words, they present the relation between the Euler and the Manakov equations using a four-to-one meromorphic map from the naive fibration to the Weierstrass normal form.
reviewed by: Shigeki Matsutani
Mathematics Subject Classification ID: 14D06
Mathematics Subject Classification ID: 14H52
Mathematics Subject Classification ID: 70E15
Mathematics Subject Classification ID: 37N05
Mathematics Subject Classification ID: 14J27
zbMATH DE Number: 6099400
zbMATH Keywords: free rigid body
zbMATH Keywords: elliptic fibration
zbMATH Keywords: Weierstrass normal form
zbMATH Keywords: quadratic intersection
zbMATH Keywords: spectral curve
zbMATH Keywords: singular fibers of Kodaira
MaRDI profile type: Publication
OpenAlex ID: W2042319780
DOI: 10.14492/HOKMJ/1351086221
description: scientific article; zbMATH DE number 6099400