Sigma Functions for a Space Curve of Type (3,4,5)

Abstract

In this article, a generalized Kleinian sigma function for an affine $(3,4,5)$ space curve of genus two was constructed as the simplest example of the sigma function for an affine space curve, and in terms of the sigma function, the Jacobi inversion formulae for the curve are obtained. An interesting relation between a space curve with a semigroup generated by $(6,13,14,15,16)$ and Norton number associated with Monster group is also mentioned in the Appendix by the second author.