2026-04-17T13:05:24Zhttps://recercat.cat/oai/request

oai:recercat.cat:2445/1974282025-12-05T09:57:56Zcom_2072_1057col_2072_478917col_2072_478920

00925njm 22002777a 4500 dc Colombo. Elisabetta author Matin, Olivier author Naranjo del Val, Juan Carlos author Pirola, Gian Pietro author 2023-05-02T08:57:49Z 2023-06-01T05:10:35Z 2022-06-01 2023-05-02T08:57:50Z Consider a very general abelian variety $A$ of dimension at least 3 and an integer $0<d \leq \operatorname{dim} A$. We show that if the map $A^k \rightarrow \mathrm{CH}_0(A)$ has a $d$-dimensional fiber then $k \geq d+(\operatorname{dim} A+1) / 2$. 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 $(3 g+1) / 2$ for $g \geq 3$, thus improving results of Alzati and the last-named author in the case of a very general abelian variety. Varietats abelianes Geometria algebraica Geometria biracional Abelian varieties Algebraic geometry Birational geometry Degree of irrationality of a very general Abelian variety