Abstract
The degree of irrationality of a projective variety 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 of degree . 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.
Citation
Nathan Chen. "Degree of irrationality of very general abelian surfaces." Algebra Number Theory 13 (9) 2191 - 2198, 2019. https://doi.org/10.2140/ant.2019.13.2191
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