Low-dimensional factors of superelliptic Jacobians

Thomas Occhipinti; Douglas Ulmer

Low-dimensional factors of superelliptic Jacobians

Algebraic Geometry 2014-10-29 v2 Number Theory

Authors: Thomas Occhipinti , Douglas Ulmer

Abstract

Given a polynomial $f\in\mathbb{C}[x]$ , we consider the family of superelliptic curves $y^d=f(x)$ and their Jacobians $J_d$ for varying integers $d$ . We show that for any integer $g$ the number of abelian varieties up to isogeny of dimension $\le g$ which appear in any $J_d$ is finite and their multiplicities are bounded.

Keywords

superelliptic curves Jacobians abelian varieties isogeny polynomial factors algebraic geometry dimension bounds

Cite

@article{arxiv.1409.7029,
  title  = {Low-dimensional factors of superelliptic Jacobians},
  author = {Thomas Occhipinti and Douglas Ulmer},
  journal= {arXiv preprint arXiv:1409.7029},
  year   = {2014}
}

Comments

6 pages. v2: Several small changes following referee report. To appear in the European Journal of Mathematics

Low-dimensional factors of superelliptic Jacobians

Abstract

Keywords

Cite

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