On the symmetric determinantal representations of the Fermat curves of prime degree

Yasuhiro Ishitsuka, Tetsushi Ito

研究成果: ジャーナルへの寄稿学術誌査読

2 被引用数 (Scopus)

抄録

We prove that the defining equations of the Fermat curves of prime degree cannot be written as the determinant of symmetric matrices with entries in linear forms in three variables with rational coefficients. In the proof, we use a relation between symmetric matrices with entries in linear forms and non-effective theta characteristics on smooth plane curves. We also use some results of Gross-Rohrlich on the rational torsion points on the Jacobian varieties of the Fermat curves of prime degree.

本文言語英語
ページ(範囲)955-967
ページ数13
ジャーナルInternational Journal of Number Theory
12
4
DOI
出版ステータス出版済み - 6月 1 2016
外部発表はい

!!!All Science Journal Classification (ASJC) codes

  • 代数と数論

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