We show that the non-Archimedean skeleton of Prym variety associated to an unramified double cover algebraic curve is naturally isomorphic (as a principally polarized tropical abelian variety) cover. This confirms conjecture by Jensen and first author. prove new upper bound on dimension Prym-Brill-Noether locus for generic covers curves with fixed even gonality base. Our methods also give proof...

Introduction: A good understanding of the geometry of a theta divisor Θ of a principally polarized abelian variety (A,Θ) requires a knowledge of properties of its canonical linear system, the Gauss linear system |OΘ(Θ)|. A striking feature of the theta divisor Θ(C) of the Jacobian of a curve C is that the dual of the branch divisor of the associated Gauss map γΘ on Θ, is not a hypersurface as e...

Given Prym-Tyurin varieties of exponent q with respect to a finite group G, a subgroup H and a set of rational irreducible representations of G satisfying some additional properties, we construct a Prym-Tyurin variety of exponent [G : H ]q in a natural way. We study an example of this result, starting from the dihedral group Dp for any odd prime p. This generalizes the construction of [4] for p...

To any pair of coverings fi : X → Xi, i = 1, 2 of smooth projective curves one can associate an abelian subvariety of the Jacobian JX , the Prym variety P (f1, f2) of the pair (f1, f2). In some cases we can compute the type of the restriction of the canonical principal polarization of JX . We obtain 2 families of Prym-Tyurin varieties of exponent 6.

Introduction 1 1. Kanev’s construction and Prym-Tyurin varieties of E6-type 7 2. The E6 lattice 11 3. Degenerations of Jacobians and Prym varieties 13 4. Degenerations of Prym-Tyurin-Kanev varieties 15 5. The global geometry of the Hurwitz space of E6-covers 20 6. The Prym-Tyurin map along boundary components of Hur 30 7. Ordinary Prym varieties regarded as Prym-Tyurin-Kanev varieties 39 8. The...

Let P ∪P ′ be the two component Prym variety associated to anétale double cover˜C → C of a non-hyperelliptic curve of genus g ≥ 6 and let |2Ξ 0 | and |2Ξ ′ 0 | be the linear systems of second order theta divisors on P and P ′ respectively. The component P ′ contains canonically the Prym curve˜C. We show that the base locus of the subseries of divisors containing˜C ⊂ P ′ is exactly the curve˜C. ...

Let P ∪P ′ be the two component Prym variety associated to an étale double cover C̃ → C of a non-hyperelliptic curve of genus g ≥ 6 and let |2Ξ0| and |2Ξ ′ 0| be the linear systems of second order theta divisors on P and P ′ respectively. The component P ′ contains canonically the Prym curve C̃. We show that the base locus of the subseries of divisors containing C̃ ⊂ P ′ is exactly the curve C̃. We...

Let P ∪P ′ be the two component Prym variety associated to anétale double cover˜C → C of a non-hyperelliptic curve of genus g ≥ 6 and let |2Ξ 0 | and |2Ξ ′ 0 | be the linear systems of second order theta divisors on P and P ′ respectively. The component P ′ contains canonically the Prym curve˜C. We show that the base locus of the subseries of divisors containing˜C ⊂ P ′ is exactly the curve˜C. ...