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 |
Section | 一般 |
Research Field |
Algebra
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Research Institution | Hitotsubashi University (2013-2014) Tokyo Institute of Technology (2010-2012) |
Principal Investigator |
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Project Period (FY) |
2010-04-01 – 2015-03-31
|
Project Status |
Completed (Fiscal Year 2014)
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Budget Amount *help |
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2014: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2013: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2012: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2011: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2010: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
|
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 / 対数幾何学 / 対数的幾何学 / logアーベル多様体 / 佐武コンパクト化 / レベル構造 |
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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Report
(6 results)
Research Products
(22 results)
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[Presentation] Log Hodge theory2011
Author(s)
Chikara Nakayama
Organizer
Number Theory Seminar
Place of Presentation
Tsinghua University(北京)
Year and Date
2011-03-28
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