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arXiv · 2609.02169

Degree of irrationality of abelian surfaces

Songsong Huang·Zhi Jiang·Xin Yang
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Abstract

Let $A$ be a complex abelian surface. We prove that $A$ admits a dominant rational map of degree three to $\PP^2$ if and only if it admits a polarization of type $(1,1)$, $(1,2)$, $(1,3)$, or $(1,6)$. Consequently, the degree of irrationality of $A$ is $3$ precisely in these four cases and is $4$ otherwise.

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Songsong Huang, Zhi Jiang, Xin Yang. 2026-09-02. Degree of irrationality of abelian surfaces. https://arxiv.org/abs/2609.02169

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