2014 Fiscal Year Final Research Report
Compactifications of moduli spaces of abelian varieties and log geometry
| Project/Area Number |
22540011
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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 | Hitotsubashi University (2013-2014)
Tokyo Institute of Technology (2010-2012) |
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Principal Investigator |
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| Project Period (FY) |
2010-04-01 – 2015-03-31
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| Keywords | アーベル多様体 / トロイダル・コンパクト化 / 対数幾何 / 対数的アーベル多様体 |
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| Outline of Final Research Achievements |
We established various theories which are necessary to construct compactifications of moduli spaces of abelian varieties by log geometry as moduli spaces of log abelian varieties. For example, the theory of proper models for log abelian varieties; in particular, we proved that a proper model always exists. We systematically analyzed torsors and log torsors on a log abelian variety, by which together with the existence of proper models we had a theory of projective models for log abelian varieties. In particular, we almost proved the existence of projective models. We obtained a whole picture of log abelian varieties over a trait. We studied the comparison of algebraic geometry and formal geometry over a log abelian variety.
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| Free Research Field |
数論幾何
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