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Bibliographic Details
Main Authors: Harashita, Shushi, Yamamoto, Yuya
Format: Preprint
Published: 2024
Subjects:
Online Access:https://arxiv.org/abs/2409.13212
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Table of Contents:
  • Igusa proved in 1958 that the polynomial determining the supersingularity of elliptic curve 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 Lauricella system (of type D) of hypergeometric differential equations in three variables.