Hyperelliptic curves of genus 3 with prescribed automorphism group
Algebraic Geometry
2012-09-14 v1
Abstract
We study genus 3 hyperelliptic curves which have an extra involution. The locus of these curves is a 3-dimensional subvariety in the genus 3 hyperelliptic moduli \H_3. We find a birational parametrization of this locus by affine 3-space. For every moduli point \p \in \H_3 such that , the field of moduli is a field of definition. We provide a rational model of the curve over its field of moduli for all moduli points \p \in \H_3 such that . This is the first time that such a rational model of these curves appears in the literature.
Keywords
Cite
@article{arxiv.1209.2938,
title = {Hyperelliptic curves of genus 3 with prescribed automorphism group},
author = {J. Gutierrez and D. Sevilla and T. Shaska},
journal= {arXiv preprint arXiv:1209.2938},
year = {2012}
}