We prove that the geometric genus of a curve in a very generic Jacobian of dimension satisfies either or . This gives a positive answer to a conjecture of Naranjo and Pirola. For small values of the second inequality can be further improved to .
@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}, pages = {735--754}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 12}, number = {3}, year = {2013}, mrnumber = {3137462}, zbl = {1300.14033}, language = {en}, url = {http://www.numdam.org/item/ASNSP_2013_5_12_3_735_0/} }
TY - JOUR AU - Marcucci, Valeria Ornella TI - On the genus of curves in a Jacobian variety JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2013 SP - 735 EP - 754 VL - 12 IS - 3 PB - Scuola Normale Superiore, Pisa UR - http://www.numdam.org/item/ASNSP_2013_5_12_3_735_0/ LA - en ID - ASNSP_2013_5_12_3_735_0 ER -
%0 Journal Article %A Marcucci, Valeria Ornella %T On the genus of curves in a Jacobian variety %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2013 %P 735-754 %V 12 %N 3 %I Scuola Normale Superiore, Pisa %U http://www.numdam.org/item/ASNSP_2013_5_12_3_735_0/ %G en %F 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, Série 5, Tome 12 (2013) no. 3, pp. 735-754. http://www.numdam.org/item/ASNSP_2013_5_12_3_735_0/
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