Degree of irrationality of a very general abelian variety. (19th January 2021) - Colombo, Elisabetta; Martin, Olivier; Naranjo, Juan Carlos; Pirola, Gian Pietro
Abstract: Consider a very general abelian variety $A$ of dimension at least $3$ and an integer $0<d≤ \dim A$ . We show that if the map $A^k→ CH_0(A)$ has a $d$ -dimensional fiber then $k≥ d+(\dim A+1)/2$ . This extends results of the second-named author which covered the cases $d=1, 2$ . As a geometric application, we prove that any dominant rational map from a very general abelian $g$ -fold to $\mathbb{P}^g$ has degree at least $(3g+1)/2$ for $g≥ 3$, thus improving results of Alzati and the last-named author in the case of a very general abelian variety.