| Project/Area Number |
08304002
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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 | Osaka University |
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Principal Investigator |
USUI Sampei Osaka, University, Graduate School of Science, Professor, 大学院・理学研究科, 教授 (90117002)
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| Co-Investigator(Kenkyū-buntansha) |
KONNO Kazuhiro Osaka University, Grad.Sch.of Sci., Associtate Professor, 大学院・理学研究科, 助教授 (10186869)
MORI Shigefumi Kyoto University, Research Institute of Math.Sci.Professor, 数理解析研究所, 教授 (00093328)
MUKAI Shigeru Nagoya University, Grad.Sch.of Math.Sci., Professor, 大学院・多元数理学研究科, 教授 (80115641)
KATO Kazuya University of Tokyo, Grad.Sch.of Math.Sci., Professor, 大学院・数理科学研究科, 教授 (90111450)
NAKAMURA Iku Hokkaido University, Grad.Sch.of Sci., Professor, 大学院・理学研究科, 教授 (50022687)
川又 雄二郎 東京大学, 大学院・数理科学研究科, 教授 (90126037)
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| Project Period (FY) |
1996 – 1998
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| Project Status |
Completed (Fiscal Year 1998)
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| Budget Amount *help |
¥6,100,000 (Direct Cost: ¥6,100,000)
Fiscal Year 1998: ¥1,800,000 (Direct Cost: ¥1,800,000)
Fiscal Year 1997: ¥1,800,000 (Direct Cost: ¥1,800,000)
Fiscal Year 1996: ¥2,500,000 (Direct Cost: ¥2,500,000)
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| Keywords | Hodge theory / Logarithmic geometry / Algebraic varieties / Pluri-canonical forms / K3 surfaces / Canonical curves / Calabi-Yau manifolds / Morsification / Hodge 理論 / Log 幾何学 / 多重標準形成 / K3曲面 / calabi-yau多様体 / Hodge構造の分類空間 / 部分コンパクト化 / 藤田の自由予想 / Calabi-Yau多様体 / Clifford指数 / Reidのflip予想 / 小平エネルギー / abel多様体の普遍族 / Log幾何とHodge構造の退化 / 単純特異点のMckay対応 / 藤田の自由性予想 / Brill-Noether軌跡と偏極K3曲面 / 半安定層の分類空間 / 標準曲面のAlbanese写像 / スペクトル・エータ写像 / 加群拡大の微分作用素による自明化 |
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| Research Abstract |
We held also this year the Research Meeting which continues more than ten years :
"Hodge Theory Log Geometry Degenerations" October 12-16, 1998, Izumigo, Yatsugatake, Kitakoma-gun. Yamanashi, Organizers : Masaniri Asakura, Tatsuya Arakawa, Sampei Usui.
The topics of this year is as in the title. There were 16 expositions on this topics and there were stimulating discussions among the participants.
We held the following mini-workshop. All participants exposed their research results an4 had stimulating discussions among them : "Hodge Theory and Algebraic Geometry", January 28-31, 1999, Edel Sasayuri, Yatiyo-cho, Tka-gun, Hyogo, Organizer : Sampei Usui.
As in the last year, we had communications with the local people including high school students in leisure time. Both of us were satisfied with these communications.
Each research result is as follows : Sampei Usui and Kazuya Kato worked together and succeeded to construct (partial) compactifications of arithmetic quotients of classifying space
… More
s of Hodge structures with arbitrary Hodge types. This is a generalization of toroidal compactifications by Mumford et al. for Hermitian symmetric domains. We are preparing the paper. Kawamata investigated the deformations of canonical singularities and the extendability of pluri-canonical forms. Mukai made an exposition on polarized K3 surfaces in Euroconference in 1998. Mori made an exposition under the title of Rational curves on algebraic varieties and K Kato made an exposition under the title of Bloch Conjecture and p-adic epsilon elements in the Final Taniguchi Symposium in Nara, December 1998. Usui made an exposition under the title of Logarithmic Hodge structures and their classifying spaces and Masahiko Saito made an exposition under the title of Prepotentials of Yukawa couplings of certain Calabi-Yau 3-folds in NATO Advanced Study Institute in Banif, June 1998. Konno succeeded to solve 1-2-3 Conjecture of Reid completely. Ashikaga and Arakawa worked together and solved the Morsifications for hyper-elliptic pencils. Usa introduced and investigated the notion of geometric shells.
The other research results are found in the list of references on the next pages. Less
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