On the genus of curves in a Jacobian variety

Abstract

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 and Pirola. For low values of g the second inequality can be further improved to p>2g-2.

arXiv comment16 pages

References in corpus (1)

• Generic Torelli theorem for Prym varieties of ramified coverings