Rational curves on quotients of abelian varieties by finite groups

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 < age(g(k)) < 1. In this paper, we show that age(g(k)) = 1 is enough to guarantee that A/< g > has at least one rational curve.