2009 Fiscal Year Final Research Report
Compactifications of moduli spaces of mixed Hodge structure and log geometry
| Project/Area Number |
18540017
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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 | Tokyo Institute of Technology |
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Principal Investigator |
NAKAYAMA Chikara Tokyo Institute of Technology, 大学院・理工学研究科, 助教 (70272664)
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| Project Period (FY) |
2006 – 2009
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| Keywords | 対数的幾何学 / 混合ホッジ構造 / ホッジ理論 / 加藤-臼井空間 / 冪零軌道 / SL(2)-軌道 |
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| Research Abstract |
We constructed the Borel-Serre compactification and the SL(2)-compactification of the moduli space of the mixed Hodge structures by the method of log geometry. The Borel-Serre compactification is constructed by the Borel-Serre orbits and has nice properties such as local compactness. The SL(2)-compactification is constructed by the SL(2)-orbits and closely related to the compactification by the nilpotent oribits (the mixed version of Kato-Usui space) via the SL(2)-orbit theorem, which associates an SL(2)-orbit to a nilpotent orbit.
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Research Products
(14 results)
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[Presentation] Log abelian varieties2007
Author(s)
Takeshi Kajiwara, Chikara Nakayama
Organizer
p-adic method and its applications in arithmetic geometry, 2007
Place of Presentation
東京大学駒場キャンパス
Year and Date
2007-06-12
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