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October 2012 Some elliptic fibrations arising from free rigid body dynamics
Isao NARUKI, Daisuke TARAMA
Hokkaido Math. J. 41(3): 365-407 (October 2012). DOI: 10.14492/hokmj/1351086221

Abstract

An elliptic fibration over P3($¥mathbb{C}$), naively arising from the Euler equation for free rigid body dynamics, is studied from the viewpoint of complex algebraic geometry. With this elliptic fibration, associated is an elliptic fibration in Weierstraß normal form, whose generic fibres are isomorphic to those of the original fibration. This normal form is desingularized in a canonical manner. It is shown that there is a four-to-one meromorphic mapping from the naive elliptic fibration to the Weierstraß mormal form. The latter fibration is also shown to be bimeromorphic to the family of spectral curves arising from the corresponding Manakov equation.

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Isao NARUKI. Daisuke TARAMA. "Some elliptic fibrations arising from free rigid body dynamics." Hokkaido Math. J. 41 (3) 365 - 407, October 2012. https://doi.org/10.14492/hokmj/1351086221

Information

Published: October 2012
First available in Project Euclid: 24 October 2012

zbMATH: 1276.14015
MathSciNet: MR3012456
Digital Object Identifier: 10.14492/hokmj/1351086221

Subjects:
Primary: 14D06
Secondary: 14H52, 14H70, 37J35, 70E15

Rights: Copyright © 2012 Hokkaido University, Department of Mathematics

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Vol.41 • No. 3 • October 2012
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