2023/12/28 by Ryo Ohashi, Ohashi, Ryo, Momonari Kudo +1 · 1 citation
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Cryptography and Residue Arithmetic #FOS: Computer and information sciences #FOS: Mathematics #Number Theory (math.NT) #Polynomial and algebraic computation #Symbolic Computation (cs.SC)
paper · pdf · doi:10.48550/arxiv.2312.16858
openalex publication_date 2023/12/28 · openalex created_date 2023/12/30 · openalex updated_date 2026/08/01
In algebraic geometry, enumerating or finding superspecial curves in positive characteristic p is important both in theory and in computation. In this paper, we propose feasible algorithms to enumerate or find superspecial hyperelliptic curves of genus 4 with automorphism group properly containing the Klein 4-group. Executing the algorithms on Magma, we succeeded in enumerating such superspecial curves for every p with 19 ≤ p < 500, and in finding a single one for every p with 19 ≤ p < 7000.