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# Mathematical Research Letters

## Volume 22 (2015)

### Number 4

### Rational curves on quotients of abelian varieties by finite groups

Pages: 1145 – 1157

DOI: http://dx.doi.org/10.4310/MRL.2015.v22.n4.a9

#### Authors

#### Abstract

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.

Published 24 July 2015