Related papers: Prym varieties and applications
We study Prym varieties of ramified (at precisely two points) double covers of smooth irreducible complex projectives curves that admit an automorphism of prime order $p>2$. Using Galois theory, we give an explicit constructions of Prym…
The Prym map assigns to each covering of curves a polarized abelian variety. In the case of unramified cyclic covers of curves of genus two, we show that the Prym map is ramified precisely on the locus of bielliptic covers. The key…
After Jacobians of curves, Prym varieties are perhaps the next most studied abelian varieties. They turn out to be quite useful in a number of contexts. For technical reasons, there does not appear to be any systematic treatment of Prym…
The Prym variety for a branched double covering of a nonsingular projective curve is defined as a polarized abelian variety. We prove that any double covering of an elliptic curve which has more than $4$ branch points is recovered from its…
We define and investigate the tropical Prym varieties associated to unramified Galois cyclic covers of tropical curves (or equivalently metric graphs) $\tilde{\Gamma}\to \Gamma$. Our approach here is to study the tropical Prym varieties…
The Prym map of type (g,n,r) associates to every cyclic covering of degree n of a curve of genus g, ramified at a reduced divisor of degree r, the corresponding Prym variety. We show that the corresponding map of moduli spaces is…
To every double cover ramified in two points of a general trigonal curve of genus g, one can associate an \'etale double cover of a tetragonal curve of genus g+1. We show that the corresponding Prym varieties are canonically isomorphic as…
We prove the generic injectivity of the Prym map, sending a double covering of an elliptic curve ramified at r>4 points to its polarized Prym variety. For r=6 the map is birational.
Double covers of a generic genus four curve C are in bijection with Cayley cubics containing the canonical model of C. The Prym variety associated to a double cover is a quadratic twist of the Jacobian of a genus three curve X. The curve X…
Given a curve of genus 3 with an unramified double cover, we give an explicit description of the associated Prym-variety. We also describe how an unramified double cover of a non-hyperelliptic genus 3 curve can be mapped into the Jacobian…
Let $k$ be a field of characteristic zero containing a primitive $n$-th root of unity. Let $C^0_n$ be a singular plane curve of degree $n$ over $k$ admitting an order $n$ automorphism, $n$ nodes as the singularities, and $C_n$ be its…
We construct two pencils of bielliptic curves of genus three and genus five. The first pencil is associated with a general abelian surface with a polarization of type $(1,2)$. The second pencil is related to the first by an unramified…
We study the ramified Prym map $\mathcal P_{g,r} \longrightarrow \mathcal A_{g-1+\frac r2}^{\delta}$ which assigns to a ramified double cover of a smooth irreducible curve of genus $g$ ramified in $r$ points the Prym variety of the…
For a class of non-hyperelliptic genus 3 curves C which are 2-fold coverings of elliptic curves E, we give an explicit algebraic description of all birationally non-equivalent genus 2 curves whose Jacobians are degree 2 isogeneous to the…
We prove that Prym varieties of algebraic curves with two smooth fixed points of involution are exactly the indecomposable principally polarized abelian varieties whose theta-functions provide explicit formulae for integrable 2D…
We show that the Prym variety associated to a triple covering f: Y --> X of curves is principally polarized of dimension > 1, if and only if f is non-cyclic, etale and X is of genus 2. We investigate some properties of these Prym varieties…
A new relation between Prym varieties of arbitrary morphisms of algebraic curves and integrable systems is discovered. The action of maximal commutative subalgebras of the formal loop algebra of GL(n) defined on certain infinite-dimensional…
In this note, we introduce the notion of an unramified strongly cyclic covering for a cyclic curve, a class that has similar properties to, and contains, unramified double covers of hyperelliptic curves. We determine several of their basic…
Given a tame Galois branched cover of curves pi: X -> Y with any finite Galois group G whose representations are rational, we compute the dimension of the (generalized) Prym variety corresponding to any irreducible representation \rho of G.…
A well-known and difficult problem in computational number theory and algebraic geometry is to write down equations for branched covers of algebraic curves with specified monodromy type. In this article, we present a technique for computing…