Study on function fields of algebraic hypersurfaces focusing on projections, - for an evolution of Galois point theory -

2015 Fiscal Year Final Research Report

• Project/Area Number: 25400059
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Niigata University (2014-2015); Nagaoka National College of Technology (2013)
• Principal Investigator: Takahashi Takeshi 新潟大学, 自然科学系, 准教授 (60390431)
• 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, 大学院ソシオアーツアンドサイエンス研究部, 教授 (10211111) ; MIURA Kei 宇部工業高等専門学校, 一般科, 准教授 (50353321)
• Project Period (FY): 2013-04-01 – 2016-03-31
• Keywords: ガロワ点 / ガロア点 / 準ガロワ点 / 準ガロア点 / 弱ガロア・ワイエルシュトラス点 / 弱ガロワ・ワイエルシュトラス点 / 自己同型群 / ガロワ被覆

Outline of Final Research Achievements

The purpose of my work is to develop a new method for the study on function fields of projective hypersurfaces as a generalization of Galois point theory. A point is called a Galois point if the projection from the point induces a Galois extension of function fields. It was defined by Prof Yoshihara (Niigata Univ.) in 1996.
By the joint work with Prof. Miura (National Institute of Technology, Ube College) and Prof. Fukasawa (Yamagata Univ.), we defined the new notion "quasi-Galois point", which is a generalization of "Galois point", and have studied its fundamental properties. By the joint work with Prof. Komeda (Kanagawa Institute of Technology), we define the new notion "weak Galois Weierstrass point" and study the relations between these and Galois points.

Free Research Field

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