Let A be a principally polarized abelian variety of dimension four and let Θ ⊂ A be a symmetric theta-divisor, which we assume to be smooth. Using the Hodge structure on H(Θ) we associate to A two abelian subvarieties J(K) ⊂ J(H) of the intermediate jacobian J(Θ) of Θ of dimensions five and nine respectively. We show that J(H) is generated by the image under the Abel-Jacobi map of the family F ...

Our main theorem is an improvement of the Criterion of Kanev about Prym–Tyurin varieties induced by correspondences, which includes correspondences with fixed points. We give some examples of Prym–Tyurin varieties using this criterion.

We give upper and lower bounds for the number of rational points on Prym varieties over finite fields. Moreover, we determine the exact maximum and minimum number of rational points on Prym varieties of dimension 2.

We show that the Prym map for 4-th cyclic étale covers of curves of genus 4 is a dominant morphism to a Shimura variety for a family of Abelian 6-folds of Weil type. According to the result of Schoen, this implies algebraicity of Weil classes for this family.

In this paper we construct a non-trivial element in the higher Griffiths group Grif f 3,2 for the generic abelian fourfold A 4 with polarization of type (1, 2, 2, 2). The key idea is to use that A 4 can be realized as a generalized Prym variety and for this reason contains in a natural way some curves i.e. dimension 1 cycles.

Mumford defined a natural isomorphism between the intermediate jacobian of a conicbundle over P and the Prym variety of a naturally defined étale double cover of the discrminant curve of the conic-bundle. Clemens and Griffiths used this isomorphism to give a proof of the irrationality of a smooth cubic threefold and Beauville later generalized the isomorphism to intermediate jacobians of odd-di...

Let $f\colon S'\longrightarrow S$ be a cyclic branched covering of smooth projective surfaces over $\mathbb{C}$ whose branch locus $\Delta\subset is ample divisor. Pick very complete linear system $|\mathcal{H}|$ on $S$, such that the polarized surface $(S, |\mathcal{H}|)$ not scroll nor has rational hyperplane sections. For general member $[C]\in|\mathcal{H}|$ consider $\mu_{n}$-equivariant is...

Let G denote a finite group and π : Z → Y a Galois covering of smooth projective curves with Galois group G. For every subgroup H of G there is a canonical action of the corresponding Hecke algebra Q[H\G/H ] on the Jacobian of the curve X = Z/H . To each rational irreducible representation W of G we associate an idempotent in the Hecke algebra, which induces a correspondence of the curve X and ...