Gauss map on the theta divisor and Green's functions

Abstract

In an earlier paper we constructed a Cartier divisor on the theta divisor of a principally polarised abelian variety whose support is precisely the ramification locus of the Gauss map. In this note we discuss a Green's function associated to this locus. For jacobians we relate this Green's function to the canonical Green's function of the corresponding Riemann surface.

arXiv comment10 pages, in: B. Edixhoven, G. van der Geer and B. Moonen (eds.), Modular Forms on Schiermonnikoog. Cambridge University Press 2008