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Group generated by total sextactic points of Kuribayashi quartic curve
Journal of Algebra and Its Applications ( IF 0.8 ) Pub Date : 2020-07-24 , DOI: 10.1142/s021949882150184x Alwaleed Kamel 1, 2
Journal of Algebra and Its Applications ( IF 0.8 ) Pub Date : 2020-07-24 , DOI: 10.1142/s021949882150184x Alwaleed Kamel 1, 2
Affiliation
A Kuribayashi quartic curve
𝒞 a : X 4 + Y 4 + Z 4 + a ( X 2 Y 2 + Y 2 Z 2 + Z 2 X 2 ) = 0 , a ∈ ℂ ∖ { − 1 , ± 2 } ,
carries total sextactic points if and only if a = 1 4 or a is a zero of P ( a ) = a 3 + 6 8 a 2 − 9 1 a + 9 8 , cf. [1] . In [2] , the authors describe the subgroup generated by the total sextactic points in the Jacobian of a Kuribayashi quartic curve when a is a zero of P ( a ) . In this paper, we describe this group when a = 1 4 .
中文翻译:
由栗林四次曲线的总性点生成的组
栗林四次曲线
𝒞 一种 : X 4 + 是 4 + Z 4 + 一种 ( X 2 是 2 + 是 2 Z 2 + Z 2 X 2 ) = 0 , 一种 ∈ ℂ ∖ { - 1 , ± 2 } ,
当且仅当一种 = 1 4 要么一种 是零磷 ( 一种 ) = 一种 3 + 6 8 一种 2 - 9 1 一种 + 9 8 ,参见。[1] . 在[2] ,作者描述了由 Kuribayashi 四次曲线的雅可比行列中的总性点生成的子群一种 是零磷 ( 一种 ) . 在本文中,我们描述了这个组一种 = 1 4 .
更新日期:2020-07-24
中文翻译:
由栗林四次曲线的总性点生成的组
栗林四次曲线