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

T. Ayano ; V. M. Buchstaber

Funkcionalʹnyj analiz i ego priloženiâ, Tome 51 (2017) no. 3, pp. 4-21.

Résumé

The field of meromorphic functions on a sigma divisor of a hyperelliptic curve of genus $3$ is described in terms of the gradient of its sigma function. As an application, solutions of the corresponding families of polynomial dynamical systems in $C^4$ with two polynomial integrals are constructed. These systems were introduced by Buchstaber and Mikhailov on the basis of commuting vector fields on the symmetric square of algebraic curves.

Détail

Keywords: Abelian functions, hyperelliptic sigma functions, polynomial dynamical systems, commuting vector fields, symmetric products of algebraic curves.

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