On the genus of curves in a Jacobian variety
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 12 (2013) no. 3, p. 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.

Published online : 2019-02-21
Classification:  14H40,  32G20
@article{ASNSP_2013_5_12_3_735_0,
     author = {Marcucci, Valeria Ornella},
     title = {On the genus of curves in a Jacobian variety},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 12},
     number = {3},
     year = {2013},
     pages = {735-754},
     zbl = {1300.14033},
     mrnumber = {3137462},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2013_5_12_3_735_0}
}
Marcucci, Valeria Ornella. On the genus of curves in a Jacobian variety. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 12 (2013) no. 3, pp. 735-754. http://www.numdam.org/item/ASNSP_2013_5_12_3_735_0/

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