Consider a very general abelian variety A of dimension at least 3 and an integer 0 < d ≤ dimA. We show that if the map Ak → CH0(A) has a d-dimensional fiber then k ≥ d + (dimA + 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 Pg 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.
Degree of irrationality of a very general abelian variety
Martin, Olivier;Naranjo, Juan Carlos;Pirola, Gian Pietro
2022-01-01
Abstract
Consider a very general abelian variety A of dimension at least 3 and an integer 0 < d ≤ dimA. We show that if the map Ak → CH0(A) has a d-dimensional fiber then k ≥ d + (dimA + 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 Pg 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.File in questo prodotto:
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