Let π : Z → X be a Galois covering of smooth projective curves with Galois group the Weyl group of a simple and simply connected Lie group G. For any dominant weight λ consider the curve Y = Z/Stab(λ). The Kanev correspondence defines an abelian subvariety Pλ of the Jacobian of Y . We compute the type of the polarization of the restriction of the canonical principal polarization of Jac(Y ) to P...

This survey discusses the geometry of the moduli space of Prym varieties. Several applications of Pryms in algebraic geometry are presented. The paper begins with with a historical discussion of the life and achievements of Friedrich Prym. Topics treated in subsequent sections include singularities and Kodaira dimension of the moduli space, syzygies of Prym-canonical embedding and the geometry ...

For the Jacobian of a curve, the Riemann singularity theorem gives a geometric interpretation of the singularities of the theta divisor in terms of special linear series on the curve. This paper proves an analogous theorem for Prym varieties. Applications of this theorem to cubic threefolds, and Prym varieties of dimension five, are also considered.

We construct pointed Prym–Brill–Noether varieties parametrizing line bundles assigned to an irreducible étale double covering of a curve with prescribed minimal vanishing at fixed point. realize them as degeneracy loci in type D and deduce their classes case expected dimension. Thus, we determine Prym–Petri map prove version the theorem implying that dimension holds general case. These results ...

We present a Prym construction which associates abelian varieties to vertex-transitive strongly regular graphs. As an application we construct Prym-Tyurin varieties of arbitrary exponent ≥ 3, generalizing a result by Lange, Recillas and Rochas.

According to [LO], the Prym variety of any non-cyclic étale triple cover f : Y → X of a smooth curve X of genus 2 is a Jacobian variety of dimension 2. This gives a map from the moduli space of such covers to the moduli space of Jacobian varieties of dimension 2. We extend this map to a proper map Pr of a moduli space S3M̃2 of admissible S3-covers of genus 7 to the moduli space A2 of principally...

For the Jacobian of a curve, the Riemann singularity theorem gives a geometric interpretation of the singularities of the theta divisor in terms of special linear series on the curve. This paper proves an analogous theorem for Prym varieties. Applications of this theorem to cubic threefolds, and Prym varieties of dimension five, are also considered.

We study the ramified Prym map [Formula: see text] which assigns to a double cover of smooth irreducible curve genus in points variety covering. focus on six cases where dimension source is strictly greater than target giving geometric description generic fiber. also give an explicit example totally geodesic component fiber text].

We construct two pencils of bielliptic curves genus three and five. The first pencil is associated with a general abelian surface polarization type $(1,2)$. second related to the by an unramified double cover, Prym variety which canonically isomorphic Jacobian very curve two. Our results are obtained analyzing suitable elliptic fibrations on Kummer surfaces rational covers among them.

We work over C, the field of complex numbers. The Prym variety of a double cover C → D of a smooth connected projective curve D by a smooth connected curve C is defined (see [7]) as the identity component of the kernel of the norm homomorphism N : J(C) → J(D) between the Jacobians of the curves. This is an abelian variety polarised by the restriction of the canonical polarisation on J(C); we de...