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≤ A . We show that if the map A^k→ CH_0(A) has a d -dimensional fiber then k≥ d+(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 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.