Work

The multiplicity-one theorem for the superspeciality of curves of genus two

Year: 2025

Type: article

Abstract: Igusa proved in 1958 that the polynomial determining the supersingularity of elliptic curves in Legendre form is separable. In this paper, we get an analogous result for curves of genus 2 in Rosenhain form. More precisely we show that the ideal determining the superspeciality of the curve has multiplicity one at every superspecial point. Igusa used a Picard-Fucks differential operator annihilating a Gauß hypergeometric series. We shall use the Lauricella system (of type D) of hypergeometric differential equations in three variables.

Source: Finite Fields and Their Applications

DOI: 10.1016/j.ffa.2025.102738

Authors: Shushi Harashita, Yuya Yamamoto

Institution: Yokohama National University

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,720

Funder: Japan Society for the Promotion of Science