DAGA Seminar: On a conjecture of Naranjo and Pirola

Thursday 6 March 2012 - Valeria Marcucci


Thursday March 6, 2012, h.10:30, room SR VII
Valeria Marcucci (Pavia)
"On a conjecture of Naranjo and Pirola"

We will deal with the possible genus of a curve in a generic Jacobian variety. Given a birational morphism ?:D?J, where D is a complex smooth projective curve and J is a generic Jacobian of dimension g?4, we will show that the genus of D satisfies either g(D)=g, or g(D)?2g?2. This gives a positive answer to a conjecture of J.C. Naranjo and G.P. Pirola, who proved an analogous result for Prym varieties. We will then discuss whether the above result can be improved. There are some obstructions to the existence of curves of genus 2g?2 on J and this is related to a property of Prym varieties of ramified coverings.

Rif. int. A. Bertapelle

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