The Toda lattice, Dynkin diagrams, singularities and Abelian varieties (Q1173792)

Consider the periodic Toda lattices corresponding to extended Dynkin diagrams [cf. \textit{M. A. Ol'shanetsky} and \textit{A. M. Peremolov}, Invent. Math. 54, 261-269 (1979; Zbl 0419.58008)]. The level variety is generically an open part of an Abelian variety. The main theme of this article is that the divisor at infinity is entirely specified by the Dynkin diagram. For example, the components are canonically in bijection with the vertices and the intersection of these components can be described in combinatoric terms. The case of 3-particle Toda lattices is given in great details.