2011 Fiscal Year Final Research Report
Study on the various structures of algebraic surfaces by Galois embeddings
| Project/Area Number |
21540033
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Niigata University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
TOKUNAGA Hiroo 首都大学東京, 理工学研究科, 教授 (30211395)
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| 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, 准教授 (90332824)
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| Project Period (FY) |
2009 – 2011
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| Keywords | 代数幾何学 / ガロワ埋め込み / 代数曲面 / ガロワ群 / 分岐被覆 |
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| Research Abstract |
Suppose an abelian surface A has a Galois embedding. Then, what is the least number n such that A is embedded into the projective n-space? The answer is 7 and moreover such an abelian surface is isomorphic to E×E, where E is an elliptic curve. We considered also the questions for curves. For the plane curve with genus 1 we found the Galois group when it has a Galois point, for the space elliptic curve we found it has always Galois lines.
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