• Search Research Projects
  • Search Researchers
  • How to Use
  1. Back to previous page

Compactifications of Mumford-Tate domains and log geometry

Research Project

Project/Area Number 16K05093
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Algebra
Research InstitutionHitotsubashi University

Principal Investigator

NAKAYAMA Chikara  一橋大学, 大学院経済学研究科, 教授 (70272664)

Project Period (FY) 2016-04-01 – 2022-03-31
Project Status Completed (Fiscal Year 2021)
Budget Amount *help
¥3,250,000 (Direct Cost: ¥2,500,000、Indirect Cost: ¥750,000)
Fiscal Year 2020: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2019: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2018: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2017: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2016: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Keywordsホッジ理論 / 代数幾何
Outline of Final Research Achievements

We construct various compactifications of the Mumford-Tate domain (variants of the period domains with the actions of algebraic groups) as moduli spaces of mixed log Hodge structures endowed with the action of algebraic groups. In this process, the compactification of nilpotent orbits, the compactification by SL(2)-orbits and the compactification by Borel-Serre orbits are constructed, and the fundamental diagram including these spaces is established.

Academic Significance and Societal Importance of the Research Achievements

ある数学的対象全部の集合に自然な空間構造を入れたものをモジュライ空間といい、モジュライ空間を調べやすくするために無限遠点を追加してコンパクト化することが重要である。log 幾何は各種モジュライ空間のコンパクト化を構成する広く一般的な枠組みを提供する。本研究では log 幾何を応用し、従来構成されていなかった、混合マンフォード-テイト領域のコンパクト化に成功した。

Report

(7 results)
  • 2021 Annual Research Report   Final Research Report ( PDF )
  • 2020 Research-status Report
  • 2019 Research-status Report
  • 2018 Research-status Report
  • 2017 Research-status Report
  • 2016 Research-status Report
  • Research Products

    (21 results)

All 2021 2020 2019 2018 2017 Other

All Int'l Joint Research (5 results) Journal Article (11 results) (of which Int'l Joint Research: 7 results,  Peer Reviewed: 11 results,  Open Access: 2 results,  Acknowledgement Compliant: 3 results) Presentation (4 results) (of which Invited: 4 results) Book (1 results)

  • [Int'l Joint Research] シカゴ大学(米国)

    • Related Report
      2021 Annual Research Report
  • [Int'l Joint Research] シカゴ大学(米国)

    • Related Report
      2020 Research-status Report
  • [Int'l Joint Research] シカゴ大学(米国)

    • Related Report
      2019 Research-status Report
  • [Int'l Joint Research] シカゴ大学(米国)

    • Related Report
      2018 Research-status Report
  • [Int'l Joint Research] シカゴ大学(米国)

    • Related Report
      2017 Research-status Report
  • [Journal Article] Logarithmic abelian varieties, Part VII: Moduli2021

    • Author(s)
      Takeshi Kajiwara, Kazuya Kato, Chikara Nakayama
    • Journal Title

      Yokohama Mathematical Journal

      Volume: 67 Pages: 9-48

    • Related Report
      2021 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] On log motives2020

    • Author(s)
      Tetsushi, Ito ; Kazuya, Kato ; Chikara, Nakayama ; Sampei, Usui
    • Journal Title

      Tunisian Journal of Mathematics

      Volume: 2 Issue: 4 Pages: 733-789

    • DOI

      10.2140/tunis.2020.2.733

    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Taro fujisawa, Chikara Nakayama2020

    • Author(s)
      Geometric polarized log Hodge structures with a base of log rank one
    • Journal Title

      Kodai Mathematical Journal

      Volume: 43 Pages: 57-83

    • Related Report
      2019 Research-status Report
    • Peer Reviewed
  • [Journal Article] Logarithmic abelian varieties, Part VI: Projective models2019

    • Author(s)
      Takeshi Kajiwara, Kazuya Kato, Chikara Nakayama
    • Journal Title

      Yokohama Mathematical Journal

      Volume: 65

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Logarithmic abelian varieties, Part V: Projective models2018

    • Author(s)
      Takeshi Kajiwara, Kazuya Kato, Chikara Nakayama
    • Journal Title

      Yokohama Mathematical Journal

      Volume: 64

    • NAID

      120006633341

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Classifying spaces of degenerating mixed Hodge structures, IV: The fundamental diagram2018

    • Author(s)
      Kazuya Kato, Chikara Nakayama, Sampei Usui
    • Journal Title

      Kyoto Journal of Mathematics

      Volume: 印刷中

    • NAID

      120006732768

    • Related Report
      2017 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Logarithmic \'etale cohomology, II2017

    • Author(s)
      Chikara Nakayama
    • Journal Title

      Advances in Mathematics

      Volume: 314 Pages: 663-725

    • DOI

      10.1016/j.aim.2017.05.006

    • Related Report
      2017 Research-status Report
    • Peer Reviewed
  • [Journal Article] Log abelian varieties (Survey)2017

    • Author(s)
      Chikara Nakayama
    • Journal Title

      RIMS Kokyuroku Bessatsu

      Volume: B64

    • Related Report
      2017 Research-status Report 2016 Research-status Report
    • Peer Reviewed
  • [Journal Article] Categorical characterization of strict morphisms of fs log schemes2017

    • Author(s)
      Yuichiro Hoshi and Chikara Nakayama
    • Journal Title

      Mathematical Journal of Okayama University

      Volume: 59

    • NAID

      120005898804

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Classifying spaces of degenerating mixed Hodge structures, IV: The fundamental diagram2017

    • Author(s)
      Kazuya Kato, Chikara Nakayama, and Sampei Usui
    • Journal Title

      Kyoto Journal of Mathematics

      Volume: 印刷中

    • NAID

      120006732768

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Extended period domains, algebraic groups, and higher Albanese manifolds2017

    • Author(s)
      Kazuya Kato, Chikara Nakayama, and Sampei Usui
    • Journal Title

      S. Zucker's volume

      Volume: 印刷中

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Presentation] Log Hodge theory2021

    • Author(s)
      Chikara Nakayama
    • Organizer
      代数セミナー
    • Related Report
      2021 Annual Research Report
    • Invited
  • [Presentation] Geometric polarized log Hodge structures over the base of log rank one2018

    • Author(s)
      Chikara Nakayama
    • Organizer
      ワークショップ「ホッジ理論と代数幾何学」
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] Log motives and the Hodge realization2018

    • Author(s)
      Chikara Nakayama
    • Organizer
      Workshop: Log geometry, degenerations and related topics.
    • Related Report
      2017 Research-status Report
    • Invited
  • [Presentation] Log mixed Hodge 理論における無限遠点の捉え方 (1) ― Log higher Albanese manifolds ―2017

    • Author(s)
      Chikara Nakayama
    • Organizer
      ワークショップ「ホッジ理論と代数幾何学」
    • Related Report
      2017 Research-status Report
    • Invited
  • [Book] Hodge Theory and L^2-analysis2017

    • Author(s)
      Editor: Lizhen Ji
    • Total Pages
      597
    • Publisher
      Higher education press
    • ISBN
      9787040477771
    • Related Report
      2017 Research-status Report

URL: 

Published: 2016-04-21   Modified: 2023-01-30  

Information User Guide FAQ News Terms of Use Attribution of KAKENHI

Powered by NII kakenhi