2025/12/12 by Yamamoto, Yuya
Computer Science · Mathematics · Physics and Astronomy · #Polynomial and algebraic computation #Algebraic Geometry and Number Theory #Nonlinear Waves and Solitons
paper · doi:10.48550/arxiv.2512.11385
The multiplicity-one theorem for the simultaneous equations characterizing the superspeciality of hyperelliptic curves was established by Igusa in 1958 for genus one, and later extended by Harashita and Yamamoto in 2026 to genus two. In this paper, we generalize this result to arbitrary genus. Our approach employs the Lauricella system of type D for hypergeometric series in 2g-1 variables, whose truncations (up to scalar multiplication) give the entries of a Cartier-Manin matrix. The multiplicity-one theorem is obtained through an analysis of equalities involving partial derivatives of these entries.