Another Relation Between Approaches to the Schottky Problem

Abstract

The recent extensive work on different approaches to the Schottky problem has produced marked progress on several fronts. At the same time, it has become apparent that there exist very close connections between the various characterizations of Jacobian varieties described in Mumford's classic lectures {\it Curves and Their Jacobians\/}. Until now, the approach via double translation manifolds has seemed to be quite different from other approaches to the Schottky problem. The purpose of this paper is to bring this last approach ``into the fold'' as it were, and to show precisely how it relates to characterizations of Jacobians based on trisecants and flexes of the Kummer variety, and the K.P. equation.