English

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 kk, chk2,3,5,7\ch k \neq 2, 3, 5, 7. For the first time, an explicit equation of the hyperelliptic moduli for genus 3 is computed in terms of absolute invariants.

Keywords

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

R2 v1 2026-06-21T22:00:47.569Z