Development and application of Galois point theory of projective varieties

2017 Fiscal Year Final Research Report

• Project/Area Number: 26400057
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Ube National College of Technology
• Principal Investigator: MIURA Kei 宇部工業高等専門学校, 一般科, 教授 (50353321)
• Co-Investigator(Renkei-kenkyūsha): YOSHIHARA Hisao 新潟大学, 自然科学系, 名誉教授 (60114807) ; OHBUCHI Akira 徳島大学, 理工学部, 教授 (10211111) ; TOKUNAGA Hiro-o 首都大学東京, 理工学研究科, 教授 (30211395) ; TAKAHASHI Takeshi 新潟大学, 自然科学系, 准教授 (60390431)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: ガロワ点 / 準ガロワ点 / 射影代数多様体 / 代数曲線 / 自己同型群

Outline of Final Research Achievements

(1)By using the wreath product of group, we succeeded in evaluating the Galois group at a certain non-Galois point (joint work with A. Ohbuchi). (2)We defined an extended version of the Lissajous curve, and studied the structure of the extension of the function field by using the point projection. (3)We introduced the concept of quasi-Galois points (joint work with S. Fukasawa and T. Takahashi). (4)We studied curves with large automorphism group. In particular, we discussed the case where the order is 60d. (joint work with T. Harui and A. Ohbuchi). (5) We tried to integrate the birational transformation belonging to the Galois point with the study of the Cremona group.

Free Research Field

代数幾何