Linear Systems on Algebraic Curves and its Applications

2014 Fiscal Year Final Research Report

• Project/Area Number: 24540042
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: The University of Tokushima
• Principal Investigator: 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)
• Co-Investigator(Kenkyū-buntansha): KATO Takao 山口大学, 理学部, 名誉教授 (10016157)
• Co-Investigator(Renkei-kenkyūsha): KOMEDA Jiryo 神奈川工科大学, 工学部, 教授 (90162065) ; HOMMA Masaaki 神奈川大学, 工学部, 教授 (80145523) ; MIURA Kei 宇部工業高等専門学校, 一般科, 准教授 (50353321) ; TAKAHASHI Takeshi 新潟大学, 工学部, 准教授 (60390431)
• Project Period (FY): 2012-04-01 – 2015-03-31
• Keywords: 代数幾何 / 代数曲線 / ブリル＝ネーター理論 / 線形系 / 自己同型群

Outline of Final Research Achievements

研究成果の概要（英文）：We prove that every automorphism of a smooth plane curve should be homology type, decsendent type and exceptional types. After this, we prove that automorphism is a homology type automorphism if and only if a Galois point type or a point defined by a composition of Galois covering and another covering. When a projection is a composition of Galois covering and another covering, its Galois closure can be embedded in a wreath product of some typical groups. According these resulte, we can construct a Galois closure of some covering map of a smooth plane curve whose Galois group contains a Btype Coxster group.

Free Research Field

数学・代数学