An abelian surface with (1,6)-polarisation

TL;DR

This paper demonstrates that a specific Hamiltonian system's general fiber can be completed into a (1,6)-polarized abelian surface using a method from Adler-van Moerbeke and Vanhaecke.

Contribution

It applies a known method to identify the geometric structure of the fiber of a Hamiltonian system as a (1,6)-polarized abelian surface.

Findings

The general fiber completes to a (1,6)-polarized abelian surface.

The method of Adler-van Moerbeke and Vanhaecke is effective for this analysis.

The result links the Hamiltonian system to complex algebraic geometry.

Abstract

We use the method of Adler-van Moerbeke and Vanhaecke to show that the general fibre of the hamiltonian system of Dorizzi, Grammaticos and Ramani completes to a (1, 6)-polarised abelian surface.