2013 Fiscal Year Final Research Report
Moduli theoretic study of Fano varieties and Enriques surfaces
| Project/Area Number |
22340007
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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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 | Kyoto University |
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Principal Investigator |
MUKAI Shigeru 京都大学, 数理解析研究所, 教授 (80115641)
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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)
MORI Shigefumi 京都大学, 数理解析研究所, 教授 (00093328)
NAKAYAMA Noboru 京都大学, 数理解析研究所, 准教授 (10189079)
IDE Manabu 常葉学園大学, 教育学部, 講師 (90367582)
OHASHI Hisanori 東京理科大学, 理工学部, 助教 (40547006)
TAKAGI Hiromichi 東京大学, 数理科学研究科, 准教授 (30322150)
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| Project Period (FY) |
2010-04-01 – 2013-03-31
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| Keywords | 代数幾何学 / Enriques曲面 / K3曲面 / モジュライ空間 / Torelli定理 / ルート系 / Mathieu群 / アーベル曲面 |
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| Research Abstract |
As the next case of numerically trivial involution, we classified the numerically reflective involutions of Entiques surfaces into two types. One is of type E7, for which we succeeded to write down the explicit equations of their canonical elliptic fibrations. As a joint work with Hisanor Ohashi, we classified all finite groups which have a semi-symplectic action on an Enriques surface. We also classified all Enriques surfaces whose automorphism groups are virtually abelian. In both cases, the key of proof is the notion of root system of an Enriques surface. It was first defined by Nikulin in 80's and refined in this study of ours.
As for K3 surfaces of higher genus, we succeeded in proving the unirationality of the moduli space of K3 surfaces of genus 16 using the GPS compactification of the moduli space of twisted cubics.
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