Abelian Functions for Cyclic Trigonal Curves of Genus Four

Details Abelian Functions for Cyclic Trigonal Curves of Genus Four Abelian Functions for Cyclic Trigonal Curves of Genus Four

2006-12-21

arxiv.org/abs/math/0612654v1

J. Geom. Phys., v. 58, 450-467, 2008

Mathematics

Algebraic Geometry

23 pages

Scientific paper

10.1016/j.geomphys.2007.12.001

We discuss the theory of generalized Weierstrass $\sigma$ and $\wp$ functions defined on a trigonal curve of genus four, following earlier work on the genus three case. The specific example of the "purely trigonal" (or "cyclic trigonal") curve $y^3=x^5+\lambda_4 x^4 +\lambda_3 x^3+\lambda_2 x^2 +\lambda_1 x+\lambda_0$ is discussed in detail, including a list of some of the associated partial differential equations satisfied by the $\wp$ functions, and the derivation of an addition formulae.

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