1997 Fiscal Year Final Research Report Summary
Study of moduli spaces -compactification and period map
| Project/Area Number |
08454004
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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 | Nagoya University |
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Principal Investigator |
SAITO Hiroshi Nagoya University, Graduate School of Polymathematics, Assoc.Prof., 大学院多元数理科学研究科, 助教授 (80135293)
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| Co-Investigator(Kenkyū-buntansha) |
TERANISHI Yasuo Nagoya University, Graduate School of Polymathematics, Assoc.Prof., 大学院多元数理科学研究科, 助教授 (20115603)
TANIGAWA Yoshio Nagoya University, Graduate School of Polymathematics, Assoc.Prof., 大学院多元数理科学研究科, 助教授 (50109261)
FUJIWARA Kazuhiro Nagoya University, Graduate School of Polymathematics, Assoc.Prof., 大学院多元数理科学研究科, 助教授 (00229064)
NAMIKAWA Yukihiko Nagoya University, Graduate School of Polymathematics, Professor, 大学院多元数理科学研究科, 教授 (20022676)
NAITO Hisashi Nagoya University, Graduate School of Polymathematics, Assoc.Prof., 大学院多元数理科学研究科, 助教授 (40211411)
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| Project Period (FY) |
1996 – 1997
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| Keywords | moduli space / geometric invariant theory / louuded syumelric domain / period map / abelian surface / thete function / Horroch-Mumford |
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| Research Abstract |
1. We held a workshop on the moduli space in May as sheduled in Nagoya
University invitiing Profeeeors Alexeev and Sankaran. We discussed the canonical compactification of the moduli space of principally polarized abelian varieties constructed by Nakamura and Alexeev. In this study, we have constructed natural birational map between the moduli space of polarized abelian surfaces of degree 8 (resp.10) and the octahedral (resp.icosahedral) 3-fold. We found that the notion of log variety makes the construction clearer and that a complete integral system is related in the case of degree 8.
2. We defined a new quotient of algerbaic variety by an action of an algebraic group which is independent of the choice of a linearization. We are now examining this new quotient in examples.
3. Comparing the moduli space M of cubic 4-folds obtained from the geometric invariant theory with the period domain, we found a candidate for good geometric compactification M.This compactification suggests a good compactification of the moduli for K3 surfaces also.
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