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arXiv · 1306.4283

Rational curves on quotients of abelian varieties by finite groups

Bo-Hae Im·Michael Larsen
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Abstract

In [3], 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 $0<\age(g^k)<1$. In this paper, we show that $\age(g^k)=1$ is enough to guarantee that $A/\langle g\rangle$ has at least one rational curve.

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Bo-Hae Im, Michael Larsen. 2013-08-17. Rational curves on quotients of abelian varieties by finite groups. https://arxiv.org/abs/1306.4283

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