Location of Repository

## Families of genus two curves with many elliptic subcovers

### Abstract

We determine all genus 2 curves, defined over $\mathbb C$, which have simultaneously degree 2 and 3 elliptic subcovers. The locus of such curves has three irreducible 1-dimensional genus zero components in $\mathcal M_2$. For each component we find a rational parametrization and construct the equation of the corresponding genus 2 curve and its elliptic subcovers in terms of the parameterization. Such families of genus 2 curves are determined for the first time. Furthermore, we prove that there are only finitely many genus 2 curves (up to $\mathbb C$-isomorphism) defined over $\mathbb Q$, which have degree 2 and 3 elliptic subcovers also defined over $\mathbb Q$

Topics: Mathematics - Algebraic Geometry
Year: 2012
OAI identifier: oai:arXiv.org:1209.0434
Download PDF:
Sorry, we are unable to provide the full text but you may find it at the following location(s):
• http://arxiv.org/abs/1209.0434 (external link)

### Preview

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.