Study on Glois embedding of surface of non-general type

2015 Fiscal Year Final Research Report

• Project/Area Number: 24540036
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Algebra
• Research Institution: Niigata University
• Principal Investigator: Yoshihara Hisao 新潟大学, 自然科学系, フェロー (60114807)
• Co-Investigator(Kenkyū-buntansha): TOKUNAGA Hiroo 首都大学東京, 理工学研究科, 教授 (30211395)
• Co-Investigator(Renkei-kenkyūsha): KONDO Shigeyuki 名古屋大学, 多元数理科学研究科, 教授 (50186847) ; KONNO Kazuhiro 大阪大学, 理学研究科, 教授 (10186869) ; KOJIMA Hideo 新潟大学, 自然科学系, 教授 (90332824)
• Project Period (FY): 2012-04-01 – 2016-03-31
• Keywords: ガロワ埋め込み / ガロワ群 / ガロワ直線 / ガロワ閉包多様体

Outline of Final Research Achievements

We have studied Galois points for plane curves and some hypersurfaces, after that we have generalized the concept of it and defined Galois embedding of algebraic varieties. Here we study on the Galois embeddings of conclete algebraic varieties. For elliptic curve we embedd it by complete linear system and study the arrangement of Galois lines. For algebraic surface of non-general type we consider if there exists the Galois embedding, in paticular bi-elliptic surface has no Galois embedding. In case some algebraic variety has no Galois embedding, we consider the Galois closure variety, especially we take such variety as smooth cubic.

Free Research Field

代数幾何学