Gauss map on the theta divisor and Green's functions

2007/05/01 by Robin de Jong, de Jong, Robin
Mathematics · #14H42 #14H55 #14K25 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14H42 #msc:14H55 #msc:14K25

paper · pdf · doi:10.48550/arxiv.0705.0098

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

arxiv created 2012/05/02 · arxiv updated 2012/05/03

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.

Related

• The Gauss Map on Theta Divisors with Transversal A₁ Singularities
• Theta functions of arbitrary order and their derivatives
• Vector-valued modular forms and the Gauss map
• The Gauss map for bielliptic Prym varieties
• Compactified Jacobians, Abel maps and Theta divisors