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June 2020 Computational Approach to Enumerate Non-hyperelliptic Superspecial Curves of Genus 4
Momonari KUDO, Shushi HARASHITA
Tokyo J. Math. 43(1): 259-278 (June 2020). DOI: 10.3836/tjm/1502179310

Abstract

In this paper, an algorithm to enumerate non-hyperelliptic superspecial curves of genus $4$ over finite fields of characteristic $p \geq 5$ is constructed. As an application, the algorithm is used to enumerate non-hyperelliptic superspecial curves of genus $4$ over prime fields of characteristic $p \leq 11$. Thanks to the fact that the number of $\mathbb{F}_{p^a}$-isomorphism classes of superspecial curves over $\mathbb{F}_{p^a}$ of a fixed genus depends only on the parity of $a$, this paper contributes to the odd-degree case for genus $4$, whereas our previous work (Kudo-Harashita: Superspecial curves of genus $4$ in small characteristic) contributes to the even-degree case. This paper is the full-version of our conference paper (Kudo-Harashita: Enumerating Superspecial Curves of Genus $4$ over Prime Fields) presented at WCC2017.

Citation

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Momonari KUDO. Shushi HARASHITA. "Computational Approach to Enumerate Non-hyperelliptic Superspecial Curves of Genus 4." Tokyo J. Math. 43 (1) 259 - 278, June 2020. https://doi.org/10.3836/tjm/1502179310

Information

Published: June 2020
First available in Project Euclid: 18 June 2020

zbMATH: 07227189
MathSciNet: MR4121797
Digital Object Identifier: 10.3836/tjm/1502179310

Subjects:
Primary: 13P10
Secondary: 14G05, 14G15, 14G50, 14H45, 14Q05, 68W30

Rights: Copyright © 2020 Publication Committee for the Tokyo Journal of Mathematics

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Vol.43 • No. 1 • June 2020
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