Heriot-Watt University

Department of Mathematics

Weierstrass functions for the Trigonal (3,5) curve

This page (currently under construction) is intended to contain eventually a repository of results referring to Weierstrass theory for general trigonal curves of genus 4

y3 + (μ2 x +μ5) y2 + (μ1x3 + μ4x2 + μ7x + μ10) y = x5 + μ3 x4 + μ6 x3 + μ9 x2 + μ12x + μ15

At the moment the only case that has been considered is the Strictly Trigonal case, written in the form

y3 = x5 + λ4 x4 + λ3x3 + λ2x2 + λ1x + λ0

See the following paper for details of this theory:

Abelian Functions for Purely Trigonal Curves of Genus four
S. Baldwin, J. C. Eilbeck, J. Gibbons, and Y. Ônishi, math.AG/0612654, J. Geom. Phys., 58, 450--467, 2008
Some Maple data files on the (3,5) case we be placed here eventually.

Maintained by Chris Eilbeck/Heriot-Watt University, Edinburgh/ J.C.Eilbeck@hw.ac.uk