Rational curves on quotients of abelian varieties by finite groups

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 $A/⟨g⟩$ has at least one rational curve.

arXiv comment10 pages

Cited by in corpus (1)

• Smooth quotients of abelian varieties by finite groups