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A global study of the moduli spaces of abelian varieties over the ring of integers

Research Project

Project/Area Number 20340001
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionHokkaido University

Principal Investigator

NAKAMUR Iku  Hokkaido University, 大学院・理学研究院, 教授 (50022687)

Co-Investigator(Renkei-kenkyūsha) KATSURADA Hidenori  室蘭工業大学, 大学院・工学研究科, 教授 (80133792)
WENG Lin  九州大学, 大学院・数理学研究院, 教授 (60304002)
Project Period (FY) 2008 – 2010
Project Status Completed (Fiscal Year 2010)
Budget Amount *help
¥16,770,000 (Direct Cost: ¥12,900,000、Indirect Cost: ¥3,870,000)
Fiscal Year 2010: ¥5,590,000 (Direct Cost: ¥4,300,000、Indirect Cost: ¥1,290,000)
Fiscal Year 2009: ¥5,590,000 (Direct Cost: ¥4,300,000、Indirect Cost: ¥1,290,000)
Fiscal Year 2008: ¥5,590,000 (Direct Cost: ¥4,300,000、Indirect Cost: ¥1,290,000)
Keywordsモジュライ / アーベル多様体 / コンパクト化 / 安定性 / マッカイ対応 / 単純特異点 / 既約表現 / ディンキン図形 / 有限群スキーム / レベル構造 / アーペル多様体 / モジュライ空間 / 拡大ディンキン図形
Research Abstract

We proved the following in the theory of moduli of abelian varieties :
Theorem : There is another canonical compactification SQ^<toric>_<g,k> of the moduli of abelian varieties different from SQ_<g,k> constructed by us in 1999. Moreover there is a canonical bijectivebirationalmorphism from SQ^<toric>_<g,k> onto SQ_<g,k> which induces the isomorphism of their normalizations.
There was also a progress in sharpening the 2-dimensional McKay correspondence, which explains the connection with the extended Dynkin diagram.

Report

(4 results)
  • 2010 Annual Research Report   Final Research Report ( PDF )
  • 2009 Annual Research Report
  • 2008 Annual Research Report
  • Research Products

    (35 results)

All 2011 2010 2009 2008 Other

All Journal Article (18 results) (of which Peer Reviewed: 16 results) Presentation (10 results) Book (1 results) Remarks (6 results)

  • [Journal Article] On Ikeda's conjecture on the period of the Ikeda lift and its application2011

    • Author(s)
      Katsurada Hidenori ; Kawamura Hisaaki
    • Journal Title

      京都大学数理解析研究所報告集別冊『保型形式とその周期の構成と応用』

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Symmetries and the Riemann Hypothesis2010

    • Author(s)
      Weng Lin
    • Journal Title

      Advanced Studies in Pure Mathematics (Math.Soc.Japan) 58

      Pages: 173-223

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Stability and arithmetic2010

    • Author(s)
      Weng Lin
    • Journal Title

      Advanced Studies in Pure Mathematics (Math.Soc.Japan) 58

      Pages: 225-359

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] On the Andrianov type identity for power series attached to Jacobi forms and its application2010

    • Author(s)
      Katsurada Hidenori ; Kawamura Hisaaki
    • Journal Title

      ActaArithmetica 145

      Pages: 233-265

    • NAID

      120006466478

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Rankin-Selberg method and periods of modular forms2010

    • Author(s)
      Katsurada Hidenori
    • Journal Title

      MSJ Memoirs 21

      Pages: 86-114

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Another canonical compactification of the moduli space of abelian varieties2010

    • Author(s)
      Nakamura Iku
    • Journal Title

      Algebraic and Arithmetic Structures of Moduli Spaces (Sapporo, 2007), Advanced Studies of Pure Mathematics Math.Soc.Japan 58

      Pages: 69-135

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Another canonical compactification of the moduli space of abelian varieties2010

    • Author(s)
      Nakamura, Iku
    • Journal Title

      Advanced Studies in Pure Mathematics, Mathematical Society of Japan

      Volume: 158 Pages: 69-135

    • Related Report
      2010 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Another canonical compactification of the moduli space of abelian varieties2010

    • Author(s)
      Nakamura, Iku
    • Journal Title

      Advanced Studies in Pure Mathematics, Mathematical Society of Japan, 58(印刷中)

      Pages: 69-135

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] McKay correspondence2009

    • Author(s)
      Nakamura Iku
    • Journal Title

      Groups and symmetries, CRM Proc.and Lec.Notes 47

      Pages: 267-298

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Zeta functions for G2 and their zeros2009

    • Author(s)
      Suzuki Masatoshi ; Weng Lin
    • Journal Title

      Int.Math.Res.Not.IMRN 2

      Pages: 241-290

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Zeta functions for Sp(2n)2009

    • Author(s)
      Weng Lin
    • Journal Title

      J.Number Theory 129 3

      Pages: 567-579

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] The Riemann hypothesis for Weng's zeta function of Sp(4) over Q2009

    • Author(s)
      Suzuki Masatoshi
    • Journal Title

      J.Number Theory 129 3

      Pages: 551-567

    • Related Report
      2010 Final Research Report
  • [Journal Article] Ikeda's conjecture on the period of the Ikeda lift2009

    • Author(s)
      Katsurada Hidenori ; Kawamura Hisaaki
    • Journal Title

      数理解析研究所講究録 1659

      Pages: 68-81

    • Related Report
      2010 Final Research Report
  • [Journal Article] McKay correspondence2009

    • Author(s)
      Nakamura, Iku
    • Journal Title

      Centre de Recherches Mathematiques CRM Proceedings and Lecture Notes 47

      Pages: 267-298

    • Related Report
      2009 Annual Research Report
    • Peer Reviewed
  • [Journal Article] McKay correspondence2009

    • Author(s)
      Iku Nakamura
    • Journal Title

      Proc. Conference in honor of John McKay 2007CRM Monograph series, 印刷中

      Pages: 36-36

    • Related Report
      2008 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The asymptotic behavior of the Takhtajan-Zograf metric2008

    • Author(s)
      Weng Lin ; Obitsu Kunio ; To Wing-Keung
    • Journal Title

      Comm.Math.Phys.284 1

      Pages: 227-261

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] Deligne products of line bundles over moduli spaces of curves2008

    • Author(s)
      Weng Lin ; Zagier Don
    • Journal Title

      Comm.Math.Phys.281 3

      Pages: 793-803

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Journal Article] A certain Dirichlet series of Rankin-Selberg type associated with the Ikeda lifting2008

    • Author(s)
      Katsurada Hidenori ; Kawamura Hisaaki
    • Journal Title

      Journal of Number Theory 128 7

      Pages: 2025-2052

    • NAID

      120001040303

    • Related Report
      2010 Final Research Report
    • Peer Reviewed
  • [Presentation] Extended Dynkin diagram in McKay correspondence2011

    • Author(s)
      Nakamura, Iku
    • Organizer
      Arithmetic and Algebraic Geometry 2011
    • Place of Presentation
      Tokyo University 招待講演
    • Year and Date
      2011-01-20
    • Related Report
      2010 Annual Research Report
  • [Presentation] Extended Dynkin diagram in McKay correspondence2011

    • Author(s)
      Nakamura Iku
    • Organizer
      Arithmetic and Algebraic Geometry 2011
    • Place of Presentation
      University of Tokyo
    • Related Report
      2010 Final Research Report
  • [Presentation] McKay correspondence2009

    • Author(s)
      Nakamura, Iku
    • Organizer
      Seminar on Calabi-Yau
    • Place of Presentation
      Queen' University, Canada
    • Year and Date
      2009-09-03
    • Related Report
      2009 Annual Research Report
  • [Presentation] A canonical morphism from SQ_{g, K}^toric to SQ_{g, K}2009

    • Author(s)
      Nakamura, Iku
    • Organizer
      Moduli and Discrete Groups(2009.6.8-6.12, organized by Kondo and Mukai)
    • Place of Presentation
      Kyoto University
    • Year and Date
      2009-06-08
    • Related Report
      2009 Annual Research Report
  • [Presentation] Two comnactifications of moduli spaces of abelian varieties2009

    • Author(s)
      Iku Nakamura
    • Organizer
      Arithmetic and algebraic geometry related to moduli spaces
    • Place of Presentation
      University of Tokyo
    • Year and Date
      2009-01-19
    • Related Report
      2008 Annual Research Report
  • [Presentation] A canonical morphism from SQ^<tario>_<g,k> to2009

    • Author(s)
      Nakamura Iku
    • Organizer
      Moduli and SQ_<g,k> Discrete Groups
    • Place of Presentation
      Kyoto University
    • Related Report
      2010 Final Research Report
  • [Presentation] Two compactifications of moduli spaces of abelian varieties2009

    • Author(s)
      Nakamura Iku
    • Organizer
      Arithmetic and algebraic geometry related to moduli spaces
    • Place of Presentation
      University of Tokyo
    • Related Report
      2010 Final Research Report
  • [Presentation] A canonical morphism from SQg, K {toric} to SQg, K2008

    • Author(s)
      Iku Nakamura
    • Organizer
      Conference of Algebraic geometry
    • Place of Presentation
      Kyoto University
    • Year and Date
      2008-11-21
    • Related Report
      2008 Annual Research Report
  • [Presentation] Stability and compactification of moduli of abelian varieties2008

    • Author(s)
      Iku Nakamura
    • Organizer
      Colloquium of the Centre de recherches mathematiques
    • Place of Presentation
      Montreal University Canada
    • Year and Date
      2008-09-05
    • Related Report
      2008 Annual Research Report
  • [Presentation] Comnactification of moduli of abelian varieties2008

    • Author(s)
      Iku Nakamura
    • Organizer
      Seminar on Calabi Yau
    • Place of Presentation
      Queen University, Canada
    • Related Report
      2008 Annual Research Report
  • [Book] Algebraic and Arithmetic Structures of Moduli Spaces, Advanced Studies in Pure Mathematics vol.582010

    • Author(s)
      Lin Weng, I.Nakamura
    • Total Pages
      480
    • Publisher
      Mathematical Society of Japan(印刷中)
    • Related Report
      2009 Annual Research Report
  • [Remarks] 2010.5.31-6.4, Nakamura, Iku: "Moduli of elliptic curves", 集中講義,埼玉大学理工学部

    • Related Report
      2010 Final Research Report
  • [Remarks] 2009.9.3, Nakamura, Iku : "McKay correspondence", Seminar on Calalbi-Yau, Queen's University, Canada

    • Related Report
      2010 Final Research Report
  • [Remarks] 2008.11.21, Nakamura, Iku : "Acanonical morphism from SQ^<torio>_<g,k> to SQ_<g,k>", Kyoto University

    • Related Report
      2010 Final Research Report
  • [Remarks] 2008.9.11 and 18, Nakamura, Iku : "Compactification of moduli of abelian varieties", Seminar on Calalbi-Yau, Queen's University, Canada

    • Related Report
      2010 Final Research Report
  • [Remarks] 2008.9.5, Nakamura, Iku : "Stability and compactification of moduli of abelian varieties",the Centre de recherches mathematiques, Montereal University

    • Related Report
      2010 Final Research Report
  • [Remarks] ホームページのURL

    • URL

      http://www.math.sci.hokudai.ac.jp/~nakamura/indexJ.html

    • Related Report
      2010 Final Research Report

URL: 

Published: 2008-04-01   Modified: 2016-04-21  

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