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arXiv · 1902.05645

Degree of irrationality of very general abelian surfaces

Nathan Chen
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Abstract

The degree of irrationality of a projective variety $X$ is defined to be the smallest degree rational dominant map to a projective space of the same dimension. For abelian surfaces, Yoshihara computed this invariant in specific cases, while Stapleton gave a sublinear upper bound for very general polarized abelian surfaces $(A, L)$ of degree $d$. Somewhat surprisingly, we show that the degree of irrationality of a very general polarized abelian surface is uniformly bounded above by $4$, independently of the degree of the polarization. This result disproves part of a conjecture of Bastianelli, De Poi, Ein, Lazarsfeld and Ullery.

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Nathan Chen. 2019-02-15. Degree of irrationality of very general abelian surfaces. https://doi.org/10.2140/ant.2019.13.2191

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