On the genus of curves in a Jacobian variety
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 12 (2013) no. 3, pp. 735-754.

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 small values of g the second inequality can be further improved to p>2g-2.

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Classification : 14H40, 32G20
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     title = {On the genus of curves in a {Jacobian} variety},
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Marcucci, Valeria Ornella. On the genus of curves in a Jacobian variety. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 12 (2013) no. 3, pp. 735-754. http://archive.numdam.org/item/ASNSP_2013_5_12_3_735_0/

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