The object of study here is the singular locus of the theta divisor Θ of a principally polarized abelian variety (X,Θ). The special case when (X,Θ) is the Jacobian of a curve C shows that this is meaningful: singularities of Θ are closely related to the existence of special linear systems on the curve C and for curves of genus g ≥ 4 the divisor Θ is always singular. But for the general principa...

The Prym variety of a pair of coverings is defined roughly speaking as the complement of the Prym variety of one morphism in the Prym variety of another morphism. We show that this definition is symmetric and give conditions when such a Prym variety is isogenous to an ordinary Prym variety or to another such Prym variety. Moreover in order to show that these varieties actually occur we compute ...

We show that analytic torsion of smooth theta divisor is represented by a Siegel modular form characterizing the Andreotti-Mayer locus when g > 1.

Let η be a line bundle on a smooth curve X with η^2=0 such that π_η, the double covering induced by η is an etale morphism. Assume also that X_η be the Prym-canonical model of X associated to K_X.η and Q is a rank 4 quadric containing X_η. After stablishing the projective normality of the prym-canonical models of curves X with Clifford index 2, we obtain in this paper a sufficient condition for...

In the well known analogy between the theory of function fields of curves over finite fields and the arithmetic of algebraic number fields, the number theoretical analogue of a divisor on a curve is an Arakelov divisor. In this paper we introduce the notion of an effective Arakelov divisor; more precisely, we attach to every Arakelov divisor D its effectivity, a real number between 0 and 1. Thi...