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math.AG2011
Prym varieties of double coverings of elliptic curves
Valeria Ornella Marcucci, Juan Carlos Naranjo
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…
math.AG2011
On the genus of curves in a Jacobian variety
Valeria Ornella Marcucci
We prove that the geometric genus p of a curve in a very generic Jacobian of dimension g>3 satisfies either p=g or p>2g-3. This gives a positive answer to a conjecture of Naranjo a…