发表机构
Center for Complex Geometry, Institute for Basic Science (IBS)（复杂几何中心，基础科学研究院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究证明两条椭圆曲线乘积的无理性次数为3，补充了代数几何中关于曲线乘积无理性次数的相关结论。
AI 中文摘要
在本短文中，我们证明两条椭圆曲线乘积的无理性次数为3。
英文摘要
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 \(\mathbb P^2\).
CommentsI revised the paper, added references, and refined it by adding explanations. comments are welcome!
