#### Vol. 13, No. 9, 2019

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Degree of irrationality of very general abelian surfaces

### Nathan Chen

Vol. 13 (2019), No. 9, 2191–2198
##### Abstract

The degree of irrationality of a projective variety $X$ is defined to be the smallest degree of a 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 $\left(A,L\right)$ 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.

##### Keywords
Irrationality, abelian surface
Primary: 14K99
Secondary: 14E05