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Degree of irrationality of a very general Abelian variety

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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.

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International Mathematics Research Notices, 2022, vol. 2022, num. 11, p. 8295-8313

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Articles publicats en revistes (Matemàtiques i Informàtica)

# metadata.dc.title[].value
Degree of irrationality of a very general Abelian variety