%0 Journal Article
%T Some remarks on the hyperelliptic moduli of genus 3
%A T. Shaska
%J Mathematics
%D 2012
%I arXiv
%R 10.1080/00927872.2013.791305
%X 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 $k$, $\ch k \neq 2, 3, 5, 7$. For the first time, an explicit equation of the hyperelliptic moduli for genus 3 is computed in terms of absolute invariants.
%U http://arxiv.org/abs/1209.1237v1