Classification theory of projective varieties by Galois points and new developments
Project/Area Number |
16K05088
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Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Algebra
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Research Institution | Yamagata University |
Principal Investigator |
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Project Period (FY) |
2016-04-01 – 2019-03-31
|
Project Status |
Completed (Fiscal Year 2018)
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Budget Amount *help |
¥3,120,000 (Direct Cost: ¥2,400,000、Indirect Cost: ¥720,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
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Keywords | ガロア点 / 準ガロア点 / ガロア群 / 射影 / 射影代数多様体 / 正標数 / ガロワ点 / 自己同型群 / 代数学 |
Outline of Final Research Achievements |
(1) A criterion for the existence of a birational embedding into a projective plane with two Galois points was presented. (2) Several new examples were described, by the criterion (joint works with K. Waki and K. Higashine). (3) The arrangement of Galois lines for the Giulietti-Korchmaros curve was determined (j.w.w. Higahine). (4) A criterion for two Galois points for quotient curves was presented (j.w.w. Higashine). (5) Plane curves possessing two Galois points at which Galois groups generate a semi-direct prodocut were classified (j.w.w. P. Speziali). (6) The set of all Galois points for double-Frobeninus nonclassical curves was determined (j.w.w. H. Borges).
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Academic Significance and Societal Importance of the Research Achievements |
ガロア点は曲線の対称性を表現していると考えられます。それが複数存在するという状況を、代数関数体という代数学の標準的な言語で表現できること(判定法)を発見しました。その表現は代数幾何、群論、数論という代数学の理論を結びつけるものです。この判定法を、符号(例:QRコード)の構成に用いられている「最大曲線」にも適用し、ガロア点を複数もつことを証明しました。ここにガロア点と符号理論とのつながりが見えます。
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Report
(4 results)
Research Products
(20 results)