We prove the Prym–Green conjecture on minimal free resolutions of paracanonical curves in the case where the genus is odd.

If Σ is a smooth genus two curve, Σ ⊂ Pic(Σ) the Abel embedding in the degree one Picard variety, |2Σ| the projective space parametrizing divisors on Pic(Σ) linearly equivalent to 2Σ, and Pic(Σ)2 = G ∼= (Z/2Z) the subgroup of points of order two in the Jacobian variety J(Σ) = Pic(Σ), then G acts on |2Σ| and the quotient variety |2Σ|/G parametrizes two fundamental moduli spaces associated with t...

Given a tame Galois branched cover of curves π : X → Y with any finite Galois group G whose representations are rational, we compute the dimension of the (generalized) Prym variety Prymρ(X) corresponding to any irreducible representation ρ of G. This formula can be applied to the study of algebraic integrable systems using Lax pairs, in particular systems associated with Seiberg-Witten theory. ...

Calculations for a set of nuclear multifragmentation data are made using a Canonical and a Grand Canonical Model. The physics assumptions are identical but the Canonical Model has an exact number of particles, whereas, the Grand Canonical Model has a varying number of particles, hence, is less exact. Interesting differences are found. Typeset using REVTEX 1

A nice feature for a type of models for relations is the possibility to assign to each relation a unique, natural model. Such a model could be regarded as a canonical model for that relation. In this paper we will show that all relations without strict symmetry that can be modeled by positional models, have canonical positional models, but that for some other relations we have reasons to doubt ...

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 ...

Contents 1. Introduction 2 2. Prym varieties for covers of curves 3 3. Galois covers 8 4. Degree two covers 10 5. Covers of degree three 13 6. Covers of degree four 15 6.1. The cyclic case 15 6.2. The Klein case 17 7. The dihedral case 22 7.1. The bigonal construction 34 8. The alternating case 37 8.1. The trigonal construction for the case A 4 43 9. The symmetric case 44 9.1. The classical cas...