Algebraic geometry of the three-state chiral potts model

For more than a decade now, the chiral Potts model in statistical mechanics has attracted much attention. A number of mathematical physicists have written quite extensively about it. The solutions give rise to a curve over ℂ, and much effort has gone into studying the curve and its Jacobian. In this article, we give yet another approach to this celebrated problem. We restrict attention to the three-state case, which is simplest. For the first time in its history, we study the model with the tools of modern algebraic geometry. Aside from simplifying and explaining the previous results on the periods and Theta function of this curve, we obtain a far more complete description of the Jacobian.