Some remarks on the hyperelliptic moduli of genus 3
Algebraic Geometry
2014-05-22 v1
Abstract
In 1967, Shioda \cite{Shi1} determined the ring of invariants of binary octavics and their syzygies using the symbolic method. We discover that the syzygies determined in \cite{Shi1} are incorrect. In this paper, we compute the correct equations among the invariants of the binary octavics and give necessary and sufficient conditions for two genus 3 hyperelliptic curves to be isomorphic over an algebraically closed field , . For the first time, an explicit equation of the hyperelliptic moduli for genus 3 is computed in terms of absolute invariants.
Cite
@article{arxiv.1209.1237,
title = {Some remarks on the hyperelliptic moduli of genus 3},
author = {T. Shaska},
journal= {arXiv preprint arXiv:1209.1237},
year = {2014}
}
Comments
arXiv admin note: text overlap with arXiv:1209.0446