2007 Fiscal Year Final Research Report Summary
The global geometry of moduli spaoes
| Project/Area Number |
16204001
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| Research Category |
Grant-in-Aid for Scientific Research (A)
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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 | Hokkaido University |
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Principal Investigator |
NAKAMURA Iku Hokkaido University, Faculty of Science,Hokkaido University, Professor (50022687)
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| Co-Investigator(Kenkyū-buntansha) |
YOSHIOKA Kota Kobe University, Faculty of Science, Professor (40274047)
KONDO Shigeyuki Nagoya University, Graduate School of Mathematics, Professor (50186847)
WENG Lin Kyushu University, Faculty of Mathematics, Associate Professor (60304002)
KATO Fumiharu Kyoto University, Department of Mathematics, Associate Professor (50294880)
MATSUMOTO Keiji Hokkaido University, Faculty of Science, Associate Professor (30229546)
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| Project Period (FY) |
2004 – 2007
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| Keywords | McKay correspondence / Moduli / Compactification / Rigid geometry / p-adic geometry / Mumford fake projective plane / K3 Surfaces / L-function |
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| Research Abstract |
Nakamura proved a new theorem on McKay correspondence of a simple singularity C2/G, G being a finite group of SL(2,C). The theorem shows certain natural modules V and Vdagger have simple structures. Among others, the structure of Vdagger explains completely the known bijetive correspondence of the extended Dynkin diagram and all the irreducible representations of G.. The paper is now in print. He also proved an important vanishing theorem for degenerate quasi-abelian varieties.
Weng is constructing a new important theory of geometric class field theory, which is modeled after Mumford's stability of GIT, Seshadri-Narashiman's theory of unitary vector bundles. In this program he defined nonabelian L-functions, and in some cases he proved a theorem analogous to Riemann hypothesis.
Kato studied with Fujiwara the fundamental theory of p-adic geometry and rigid geometry. He proved also that Mumford fake projective plane and the other known fake projective planes are among Shimura varieties.
Kondo constructed a uniformization by a 5-dimensional complex ball of the moduli of ordered 8 points of the projective line, by using Borcherds modular forms.
Matsumoto gave a very precise description of a link and its complement in S3 by using real theta functions.
Yoshioka proved a formula of counting the number of instantons on certain complex surfaces with Nakajima.
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Research Products
(62 results)
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[Book] 線形代数学2007
Author(s)
中村, 郁
Total Pages
273
Publisher
数学書房
Description
「研究成果報告書概要(和文)」より
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