2026-04-13T01:06:08Zhttps://recercat.cat/oai/requestoai:recercat.cat:2445/1974282025-12-05T09:57:56Zcom_2072_1057col_2072_478917col_2072_478920
RECERCAT
author
Colombo. Elisabetta
author
Matin, Olivier
author
Naranjo del Val, Juan Carlos
author
Pirola, Gian Pietro
2023-05-02T08:57:49Z2023-06-01T05:10:35Z2022-06-012023-05-02T08:57:50Z
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.
(c) Colombo. Elisabetta et al., 2022 info:eu-repo/semantics/openAccess
Varietats abelianes
Geometria algebraica
Geometria biracional
Abelian varieties
Algebraic geometry
Birational geometry
Degree of irrationality of a very general Abelian variety
info:eu-repo/semantics/article info:eu-repo/semantics/acceptedVersion