Colombo. ElisabettaMatin, OlivierNaranjo del Val, Juan CarlosPirola, Gian Pietro2023-05-022023-06-012022-06-011073-7928https://hdl.handle.net/2445/197428Consider 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.19 p.application/pdfeng(c) Colombo. Elisabetta et al., 2022Varietats abelianesGeometria algebraicaGeometria biracionalAbelian varietiesAlgebraic geometryBirational geometryinfo:eu-repo/semantics/article7031262023-05-02info:eu-repo/semantics/openAccess