Year: 2026
Type: preprint
Abstract: In this short paper, we prove that, for any two complex elliptic curves \(E\) and \(F\), the product \(E\times F\) has degree of irrationality \(3\). The upper bound is obtained from compatible cyclic plane-cubic models of \(E\) and \(F\): three diagonal bihomogeneous sections define a dominant rational map \(E\times F\dashrightarrow\mathbb P^2\) of degree \(3\). The lower bound follows by excluding dominant rational maps of degrees \(1\) and \(2\) from an abelian surface to \(\mathbb P^2\).
Source: arXiv (Cornell University)
Author: Lee, Yongnam
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204162947