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arXiv · 1209.1237

Some remarks on the hyperelliptic moduli of genus 3

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

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T. Shaska. 2012-09-06. Some remarks on the hyperelliptic moduli of genus 3. https://doi.org/10.1080/00927872.2013.791305

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