Degree of irrationality of very general abelian surfaces

Chen, Nathan

doi:10.2140/ant.2019.13.2191

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Degree of irrationality of very general abelian surfaces

Nathan Chen

Vol. 13 (2019), No. 9, 2191–2198

DOI: 10.2140/ant.2019.13.2191

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 $(A, L)$ 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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Keywords

Irrationality, abelian surface

Mathematical Subject Classification 2010

Primary: 14K99

Secondary: 14E05

Milestones

Received: 17 February 2019

Revised: 17 May 2019

Accepted: 25 June 2019

Published: 7 December 2019

Authors

Nathan Chen
Department of Mathematics Stony Brook University Stony Brook, NY United States

Vol. 13, No. 9, 2019