Abstract
In this paper we give a passage formula between different invariants of genus 3 hyperelliptic curves: in particular between Tsuyumine and Shioda invariants. This is needed to get modular expressions for Shioda invariants, that is, for example, useful for proving the correctness of numerically computed equations of CM genus 3 hyperelliptic curves. On the other hand, we also get Shioda invariants described in terms of differences of roots of the equation defining the hyperelliptic curve, that has applications for studying the reduction type of the curve. Under certain conditions on its Jacobian, we give a criterion for determining the type of bad reduction of a genus 3 hyperelliptic curve.
Funding Statement
The author has been funded by the project PHC Bosphorus 39652NB–TÜBİTAK 117F274 and by the STIC–AmSud project 19-STIC-02.
Citation
Elisa LORENZO GARCÍA. "On different expressions for invariants of hyperelliptic curves of genus 3." J. Math. Soc. Japan 74 (2) 403 - 426, April, 2022. https://doi.org/10.2969/jmsj/83418341
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