Rational curves on quotients of abelian varieties by finite groups

Bo-Hae Im; Michael Larsen

Rational curves on quotients of abelian varieties by finite groups

Algebraic Geometry 2013-08-20 v4

Authors: Bo-Hae Im , Michael Larsen

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.

Keywords

abelian varieties quotients finite groups rational curves uniruled age invariant automorphisms

Cite

@article{arxiv.1306.4283,
  title  = {Rational curves on quotients of abelian varieties by finite groups},
  author = {Bo-Hae Im and Michael Larsen},
  journal= {arXiv preprint arXiv:1306.4283},
  year   = {2013}
}

Comments

10 pages

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