A global study of the moduli spaces of abelian varieties over the ring of integers
| Project/Area Number |
20340001
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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 | Hokkaido University |
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Principal Investigator |
NAKAMUR Iku Hokkaido University, 大学院・理学研究院, 教授 (50022687)
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| Co-Investigator(Renkei-kenkyūsha) |
KATSURADA Hidenori 室蘭工業大学, 大学院・工学研究科, 教授 (80133792)
WENG Lin 九州大学, 大学院・数理学研究院, 教授 (60304002)
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| Project Period (FY) |
2008 – 2010
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| Project Status |
Completed (Fiscal Year 2010)
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| Budget Amount *help |
¥16,770,000 (Direct Cost: ¥12,900,000、Indirect Cost: ¥3,870,000)
Fiscal Year 2010: ¥5,590,000 (Direct Cost: ¥4,300,000、Indirect Cost: ¥1,290,000)
Fiscal Year 2009: ¥5,590,000 (Direct Cost: ¥4,300,000、Indirect Cost: ¥1,290,000)
Fiscal Year 2008: ¥5,590,000 (Direct Cost: ¥4,300,000、Indirect Cost: ¥1,290,000)
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| Keywords | モジュライ / アーベル多様体 / コンパクト化 / 安定性 / マッカイ対応 / 単純特異点 / 既約表現 / ディンキン図形 / 有限群スキーム / レベル構造 / アーペル多様体 / モジュライ空間 / 拡大ディンキン図形 |
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| Research Abstract |
We proved the following in the theory of moduli of abelian varieties :
Theorem : There is another canonical compactification SQ^<toric>_<g,k> of the moduli of abelian varieties different from SQ_<g,k> constructed by us in 1999. Moreover there is a canonical bijectivebirationalmorphism from SQ^<toric>_<g,k> onto SQ_<g,k> which induces the isomorphism of their normalizations.
There was also a progress in sharpening the 2-dimensional McKay correspondence, which explains the connection with the extended Dynkin diagram.
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Report
(4 results)
Research Products
(35 results)
