CHARACTERIZATIONS OF JACOBIANS OF CURVES WITH AUTOMORPHISMS

Abstract

We obtain a characterization of theta functions of Jacobian varieties of curves with automorphisms among theta functions of principally polarized abelian varieties (p p a v) We first give a characterization m terms of finite dimensional orbits for a suitable action in the Sato Grassmannian Secondly, the Introduction of formal Baker-Akhiezer functions and formal tau-functions attached to a p p a v (for the multipuncture case) allows us to characterize, in terms of bilinear identities, those Baker-Akhiezer functions that are Baker-Akhiezer functions of Jacobians of curves with automorphisms Further; in the case of automorphisms with fixed points, we rewrite the previous result as a hierarchy of partial differential equations for the tau-function of a p pav Finally, since Baker-Akhiezer and tau functions are written in terms of theta functions, these results give rise to characterizations of p p a v in terms of their theta functions