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On Rosenhain–Göpel Configurations and Integrable Systems
Luis A. Piovan Departamento de Matemática, Universidad Nacional del Sur
8000 Bahía Blanca, Argentina
Abstract:
We give a birational morphism between two types of genus 2 Jacobians in ${\mathbb P}^{15}$. One of them is related to an Algebraic Completely Integrable System: the Geodesic Flow on $SO(4)$, metric II (so termed after Adler and van Moerbeke). The other Jacobian is related to a linear system in $|4 \Theta|$ with 12 base points coming from a Göpel tetrad of 4 translates of the $\Theta$ divisor. A correspondence is given on the base spaces so that the Poisson structure of the $SO(4)$ system can be pulled back to the family of Göpel Jacobians.
Keywords:
integrable systems.
Received: 28.04.2010 Accepted: 21.08.2010
Citation:
Luis A. Piovan, “On Rosenhain–Göpel Configurations and Integrable Systems”, Regul. Chaotic Dyn., 16:3-4 (2011), 210–222
Linking options:
https://www.mathnet.ru/eng/rcd436 https://www.mathnet.ru/eng/rcd/v16/i3/p210
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Abstract page: | 67 |
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