from the moduli space Rg of (non-trivial) étale double coverings of curves of genus g to the moduli space Ag−1 of principally polarized abelian varieties of dimension g − 1, called the Prym map. It was shown independently by Friedman-Smith [10], Kanev [13], Welters [20] and Debarre [6], that prg is generically injective for g ≥ 7. On the other hand, Mumford showed in [16, p. 346], that the Prym...

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...

We investigate a family of correspondences associated tó etale coverings of degree 3 of hyperelliptic curves. They lead to Prym-Tyurin varieties of exponent 3. We identify these varieties and derive some consequences.

In the study of integrable systems of ODE’s arising from a Lax pair with a parameter, the constants of the motion occur as spectral curves. Many of these systems are algebraically completely integrable in that they linearize on the Jacobian of a spectral curve. In an earlier paper the authors gave a classification of the spectral curves in terms of the Weyl group and arranged the spectral curve...

We study the M-theory five-brane wrapped around the Seiberg-Witten curves for pure classical and exceptional groups given by an integrable system. Generically, the D4-branes arise as cuts that collapse to points after compactifying the eleventh dimension and going to the semiclassical limit, producing brane configurations of NS5and D4-branes with N = 2 gauge theories on the world volume of the ...

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

Abstract Let J g be the Jacobian locus and let P +1 Prym locus, in moduli space A of principally polarized abelian varieties dimension , for ≥ 7. We study extrinsic geometry ⊂ under inclusion provided by theory generalized introduced Beauville. More precisely, we address problem if certain geodesic curves, defined with respect to Siegel metric starting at a variety [ JC ] ∈ curve C M direction ...