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arXiv · 1811.05806

The field of meromorphic functions on a sigma divisor of a hyperelliptic curve of genus 3 and applications

Takanori Ayano·Victor Buchstaber
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Abstract

The field of meromorphic functions on a sigma divisor of a hyperelliptic curve of genus $3$ is described in terms of the gradient of it's sigma function. Solutions of corresponding families of polynomial dynamical systems in $\mathbb{C}^4$ with two polynomial integrals are constructed as an application. These systems were introduced in the work of V. M. Buchstaber and A. V. Mikhailov on the basis of commuting vector fields on the symmetric square of algebraic curves.

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Takanori Ayano, Victor Buchstaber. 2018-11-14. The field of meromorphic functions on a sigma divisor of a hyperelliptic curve of genus 3 and applications. https://doi.org/10.1007/s10688-017-0181-4

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