Degree of irrationality of a very general abelian variety. (19th January 2021)

• Record Type: Journal Article
• Authors: Colombo, Elisabetta; Martin, Olivier; Naranjo, Juan Carlos; Pirola, Gian Pietro
• Is Part Of: International mathematics research notices. Volume 2022:Number 11(2022)
• Page Start: 8295
• Page End: 8313
• Publication Date: 2021-01-19
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1093/imrn/rnaa358
• Languages: English
• ISSNs: 1073-7928

Abstract

Abstract: Consider a very general abelian variety $A$ of dimension at least $3$ and an integer $0<d\leq \dim A$ . We show that if the map $A^k\to CH_0(A)$ has a $d$ -dimensional fiber then $k\geq d+(\dim A+1)/2$ . 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 $(3g+1)/2$ for $g\geq 3$, thus improving results of Alzati and the last-named author in the case of a very general abelian variety.