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

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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Irrationality, abelian surface
Mathematical Subject Classification 2010
Primary: 14K99
Secondary: 14E05
Received: 17 February 2019
Revised: 17 May 2019
Accepted: 25 June 2019
Published: 7 December 2019
Nathan Chen
Department of Mathematics
Stony Brook University
Stony Brook, NY
United States