On Hyperelliptic Abelian Functions of Genus 3

Abstract

The affine ring A of the affine Jacobian variety of a hyperelliptic curve of genus 3 is studied as a D-module. The conjecture on the minimal D-free resolution previously proposed is proved in this case. As a by-product a linear basis of A is explicitly constructed in terms of derivatives of Klein's hyperelliptic pe functions.

40 pages

References in corpus (2)

• Cohomologies of Affine Jacobi Varieties and Integrable Systems
• Sigma, tau and Abelian functions of algebraic curves

Cited by in corpus (7)

• Schur function expansions of KP tau functions associated to algebraic curves
• New variables of separation for particular case of the Kowalevski top
• Abelian functions associated with genus three algebraic curves
• Deriving bases for Abelian functions
• Abelian function fields on Jacobian varieties
• Hurwitz integrality of the power series expansion of the sigma function for a telescopic curve
• On the Space of KdV Fields