Mathematical Research Letters

Volume 22 (2015)

Number 4

Rational curves on quotients of abelian varieties by finite groups

Pages: 1145 – 1157



Bo-Hae Im (Department of Mathematics, Chung-Ang University, Dongjak-Gu, Seoul, South Korea)

Michael Larsen (Department of Mathematics, Indiana University, Bloomington, In., U.S.A.)


In [4], it is proved that the quotient of an abelian variety $A$ by a finite order automorphism $g$ is uniruled if and only if some power of $g$ satisfies a numerical condition $0 \lt \textrm{age}(g^k) \lt 1$. In this paper, we show that $\textrm{age}(g^k) = 1$ is enough to guarantee that $A / \langle g \rangle$ has at least one rational curve.

Accepted 26 September 2014

Published 24 July 2015