| Project/Area Number |
15340009
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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) |
SAITO Shuji University of Tokyo, Graduate School of Mathematical Science, Professor, 大学院数理科学研究科, 教授 (50153804)
KATO Kazuya Kyoto University, Graduate School of Science, Professor, 大学院理学研究科, 教授 (90111450)
MORI Shigefumi Kyoto University, RIMS, Professor, 数理解析研究所, 教授 (00093328)
KONNO Kazuhiro Osaka University, Graduate School of Science, Professor, 大学院理学研究科, 教授 (10186869)
FUJIKI Akira Osaka University, Graduate School of Science, Professor, 大学院理学研究科, 教授 (80027383)
中村 郁 北海道大学, 大学院・理学研究科, 教授 (50022687)
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| Project Period (FY) |
2003 – 2006
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| Project Status |
Completed (Fiscal Year 2006)
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| Budget Amount *help |
¥14,300,000 (Direct Cost: ¥14,300,000)
Fiscal Year 2006: ¥3,400,000 (Direct Cost: ¥3,400,000)
Fiscal Year 2005: ¥3,400,000 (Direct Cost: ¥3,400,000)
Fiscal Year 2004: ¥3,900,000 (Direct Cost: ¥3,900,000)
Fiscal Year 2003: ¥3,600,000 (Direct Cost: ¥3,600,000)
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| Keywords | Log Hodge structure / Compactification of classifying space / period map / varieties of general typem / mixed version of SL(2)-orbit theore / open complete intersection / Jacobian ring / Beilinson's Hodge conjecture / (混合)対数ホッジ構造 / モジュライ空間 / 対数中間ヤコビ多様体 / コンパクト化 / 安定擬アーベル多様体 / ベイリンソン・ホッジ予想 / モーデル・ヴェイユ格子 / 共形ケーラー構造 / 対数的(混合)ホッジ構造 / 対数的中間ヤコビ多様体 / 対数的周期写像 / 対数的アーベル・ヤコビ写像 / ヤコビ環 / Bloch予想の対数版 / Green予想 / 国際研究者交流 / log Hodge構造のfine moduli / log manifold / minimal model / Bloch-Ogus-Kato complex / リーマン面の退化 / ガロワ点 / ツイスター空間 / Frobenius多様体 |
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| Research Abstract |
Generalizing toroidal compactifications of Hermitian symmetric domains by Mumford et al., Kazuya Kato and Usui constructed fine moduli spaces of polarized log Hodge structures (PLH, for short). Moreover, we constructed Borel-Serre compactifications and SL(2)-partial compactifications of Griffiths domains, and also a fundamental diagram of the relationship of all these enlarged spaces. This joint will be published as a book of almost 300 pages in the series of Ann. Math. Studies, Princeton University Press.
Assuming the existence of a complete fan, Usui showed that the image of the extended period map, from a compactification of moduli of varieties of general type to the moduli of PLH, is a separated complex algebraic space. This observation shows in particular that, even if the moduli space of PLH has slits in this case, the image of the extended period map does not touch with these slits. This result was published in J. Alg. Geom. in 2006. The restriction of dimension in this paper is now removed and applicable for all dimensions by a recent great advance in minimal model theory.
Generalizing SL(2)-orbit theorems of Schmid in pure case in one variable and of Cattani, Kaplan and Schmid in pure case in several variables, Kazuya Kato, Chikara Nakayama and Usui obtained SL(2)-orbit theorem in mixed case in several variables and an estimate of Hodge norm in this situation. This result is submitted.
Masanori Asakura and Shuji Saito studied the Jacobian rings of open complete intersections and solved Beilinson's Hodge conjecture for sufficiently general open complete intersections. These results were publishes in Math.Zeit., in Math.Nachr., and in publication of London Math.Soc.
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