Shaska, T. Some Remarks on the Hyperelliptic Moduli of Genus 3 <div><p>In 1967, Shioda [<a href="#CIT0020" target="_blank">20</a>] determined the ring of invariants of binary octavics and their syzygies using the symbolic method. We discover that the syzygies determined in [<a href="#CIT0020" target="_blank">20</a>] 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 <i>k</i>, char <i>k</i> ≠ 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.</p> </div> remarks;moduli;genus;hyperelliptic 2014-04-23
    https://tandf.figshare.com/articles/journal_contribution/Some_Remarks_on_the_Hyperelliptic_Moduli_of_Genus_3/1005077
10.6084/m9.figshare.1005077.v1