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A deeper understanding of moduli theory integrated by special Riemannian metrics and convex polytopes

Research Project

Project/Area Number 18K13406
Research Category

Grant-in-Aid for Early-Career Scientists

Allocation TypeMulti-year Fund
Review Section Basic Section 11020:Geometry-related
Research InstitutionKagawa University

Principal Investigator

Yotsutani Naoto  香川大学, 教育学部, 准教授 (00806755)

Project Period (FY) 2018-04-01 – 2024-03-31
Project Status Completed (Fiscal Year 2023)
Budget Amount *help
¥4,160,000 (Direct Cost: ¥3,200,000、Indirect Cost: ¥960,000)
Fiscal Year 2021: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Keywords球形多様体 / 複素構造変形理論 / トーリック多様体 / 凸多面体の三角形分割 / ケーラー計量 / Bott多様体 / 凸多面体上のBernstein測度 / GKZ-理論 / ケーラー多様体 / K3曲面 / ボット多様体 / GIT-安定性 / モジュライ空間 / ファノ多様体 / カラビ-ヤウ多様体 / T-variety / δ不変量 / Fano多様体 / Gluing構成 / トーリック幾何学 / 自己同型群 / 特殊リーマン計量 / モジュライ理論
Outline of Final Research Achievements

I clarified the diffeomorphism classes of the Calabi-Yau 3-folds we constructed in 2014. Furthermore, we proved that if a simple normal crossing complex surface with the trivial canonical bundle satisfies a certain condition, there exists a family of global smoothings in a differential geometrical sense. Through this collaborative work, we also constructed some concrete examples.
Meanwhile, I proved that asymptotic Chow semistability implies that Ding polystability for any Gorensitein toric fano varieties. Also, I proved that the additivity of the Mabuchi constant for the product of toric manifolds in terms of the associated moment polytopes. Building upon these research achievements and my experience in these calculations, we classified (a) all strong Calabi dream Bott manifolds , and (b) 3 or 4-dimensional toric Fano manifolds in terms of relative K/Ding stabilities.

Academic Significance and Societal Importance of the Research Achievements

一般に与えられた代数多様体がGIT-安定か否かを判定する事は,トーリックの場合でも非常に難しい.これは対応する凸多面体上の積分値を具体的に計算する必要性が生じるためであり,この困難を部分的ではあるが克服した点や,複素構造変形理論の重要性を再吟味しつつ,正規交叉カラビ-ヤウ多様体の代数幾何的スムージング理論を特殊な状況下で微分幾何的に再現・具体例を発見した点は意義深い.特に「凸多面体の幾何学的不変量を如何に効率的に測るか?」という問題は純粋数学のみならず,工学や確率論とも密接な関係がある.ゆえに,幾何学の枠組みに捉われず分野を超えた交流による相互のインプットが大きな社会的意義を与える筈である.

Report

(7 results)
  • 2023 Annual Research Report   Final Research Report ( PDF )
  • 2022 Research-status Report
  • 2021 Research-status Report
  • 2020 Research-status Report
  • 2019 Research-status Report
  • 2018 Research-status Report
  • Research Products

    (55 results)

All 2024 2023 2022 2021 2020 2019 2018 Other

All Int'l Joint Research (14 results) Journal Article (13 results) (of which Int'l Joint Research: 6 results,  Peer Reviewed: 10 results,  Open Access: 4 results) Presentation (27 results) (of which Int'l Joint Research: 7 results,  Invited: 12 results) Remarks (1 results)

  • [Int'l Joint Research] Institute for Basic Science, CCG(韓国)

    • Related Report
      2023 Annual Research Report
  • [Int'l Joint Research] Universite de Montpellier(フランス)

    • Related Report
      2023 Annual Research Report
  • [Int'l Joint Research] 北京大学/湖南大学(中国)

    • Related Report
      2022 Research-status Report
  • [Int'l Joint Research] Lomonosov Moscow State University(ロシア連邦)

    • Related Report
      2022 Research-status Report
  • [Int'l Joint Research] Hongik大学/IBS Center for Geometry and Physics(韓国)

    • Related Report
      2022 Research-status Report
  • [Int'l Joint Research] 北京大学/湖南大学(中国)

    • Related Report
      2021 Research-status Report
  • [Int'l Joint Research] UQAM(Universite du Quebec a Montreal)(カナダ)

    • Related Report
      2021 Research-status Report
  • [Int'l Joint Research] Hongik大学(韓国)

    • Related Report
      2021 Research-status Report
  • [Int'l Joint Research] 湖南大学/北京大学(中国)

    • Related Report
      2020 Research-status Report
  • [Int'l Joint Research] UQAM(カナダ)

    • Related Report
      2020 Research-status Report
  • [Int'l Joint Research] Hongik大学(韓国)

    • Related Report
      2020 Research-status Report
  • [Int'l Joint Research] Hongik University(韓国)

    • Related Report
      2019 Research-status Report
  • [Int'l Joint Research] Peking University(中国)

    • Related Report
      2019 Research-status Report
  • [Int'l Joint Research] 北京大学/湖南大学(中国)

    • Related Report
      2018 Research-status Report
  • [Journal Article] Strong Calabi dream Bott manifolds2024

    • Author(s)
      Fujita Kento、Yotsutani Naoto
    • Journal Title

      ANNALI DELL'UNIVERSITA' DI FERRARA

      Volume: - Issue: 3 Pages: 607-630

    • DOI

      10.1007/s11565-023-00484-3

    • Related Report
      2023 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Asymptotic Chow Semistability Implies Ding Polystability for Gorenstein Toric Fano Varieties2023

    • Author(s)
      Yotsutani Naoto
    • Journal Title

      Mathematics

      Volume: 11 Issue: 19 Pages: 4114-4114

    • DOI

      10.3390/math11194114

    • Related Report
      2023 Annual Research Report
    • Peer Reviewed / Open Access
  • [Journal Article] Diffeomorphism classes of the doubling Calabi-Yau threefolds with Picard number two2023

    • Author(s)
      Yotsutani Naoto
    • Journal Title

      Rendiconti del Circolo Matematico di Palermo Series 2

      Volume: 856

    • Related Report
      2022 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Differential geometric global smoothings of simple normal crossing complex surfaces with trivial canonical bundle2023

    • Author(s)
      Doi Mamoru、Yotsutani Naoto
    • Journal Title

      Complex Manifolds

      Volume: 10 Issue: 1

    • DOI

      10.1515/coma-2022-0143

    • Related Report
      2022 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Relative Ding and K-stability of toric Fano manifolds in low dimensions2023

    • Author(s)
      Yasufumi Nitta, Shunsuke Saito and Naoto Yotsutani
    • Journal Title

      European Journal of Mathematics

      Volume: 9 Issue: 2

    • DOI

      10.1007/s40879-023-00617-0

    • Related Report
      2022 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Corrigenda: Relative algebro-goemetric stabilities of toric manifolds(TOHOKU MATH. J. 71 (2019), 495-524)2023

    • Author(s)
      Yotsutani Naoto, Zhou Bin
    • Journal Title

      Tohoku Math Journal

      Volume: 75 Pages: 1-5

    • Related Report
      2022 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Corrigenda to "Doubling construction of Caleb-Yau threefolds"2021

    • Author(s)
      Mamoru Doi, Naoto Yotsutani
    • Journal Title

      New York Journal of Mathematics

      Volume: 27 Pages: 475-476

    • Related Report
      2020 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] A summary of global smoothings of normal crossing complex surfaces2020

    • Author(s)
      Naoto Yotsutani
    • Journal Title

      代数幾何学シンポジウム記録2020

      Volume: 2020 Pages: 11-23

    • NAID

      120006952795

    • Related Report
      2020 Research-status Report
    • Open Access
  • [Journal Article] On uniform K-stability of pairs for algebraic curves2019

    • Author(s)
      Naoto Yotsutani
    • Journal Title

      RIMS Kokyuroku

      Volume: 2140 Pages: 80-93

    • Related Report
      2019 Research-status Report
  • [Journal Article] Relative Algebra-Geomteric stabilities of toric manifolds2019

    • Author(s)
      Naoto Yotsutani, Bin Zhou
    • Journal Title

      Tohoku Mathematical Journal

      Volume: 71 Pages: 495-524

    • Related Report
      2019 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Gluing construction of compact Spin(7)-manifolds2019

    • Author(s)
      Mamoru Doi and Naoto Yotsutani
    • Journal Title

      Journal of the Mathematical Society of Japan

      Volume: 71 Issue: 2 Pages: 349-382

    • DOI

      10.2969/jmsj/77007700

    • NAID

      130007636381

    • ISSN
      0025-5645, 1881-1167, 1881-2333
    • Related Report
      2018 Research-status Report
    • Peer Reviewed
  • [Journal Article] Relative Algebro-Geometric stabilities of toric manifolds2019

    • Author(s)
      Naoto Yotsutani and Zhou Bin
    • Journal Title

      Tohoku Mathematical Journal

      Volume: 印刷中

    • Related Report
      2018 Research-status Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] On the relation between uniform K-stability and Chow stability of toric varieties2018

    • Author(s)
      Naoto Yotsutani
    • Journal Title

      なし

      Volume: 2098 Pages: 60-67

    • Related Report
      2018 Research-status Report
  • [Presentation] Numerical semistability of projective toric varieties2024

    • Author(s)
      Yotsutani Naoto
    • Organizer
      Workshop on Fano spherical varieties - 2024
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Semistable pairs of projective toric varieties2024

    • Author(s)
      Yotsutani Naoto
    • Organizer
      Advances in special Kahler metrics
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Chow stability and non-symmetric toric Fano manifolds2023

    • Author(s)
      Yotsutani Naoto
    • Organizer
      IBS Center for Complex Geometry Seminar
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Semistable pairs of projective toric varieties2023

    • Author(s)
      Yotsutani Naoto
    • Organizer
      The 8th China-Japan Geometry Conference
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Semistable pairs of projective toric varieties2023

    • Author(s)
      Yotsutani Naoto
    • Organizer
      Peking University Geometric Analysis seminar
    • Related Report
      2023 Annual Research Report
    • Int'l Joint Research
  • [Presentation] Chow stability of λ-stable toric varieties2023

    • Author(s)
      Yotsutani Naoto
    • Organizer
      福井大学幾何学セミナー
    • Related Report
      2023 Annual Research Report
    • Invited
  • [Presentation] Bott Manifolds with the Strong Calabi Dream Structure2023

    • Author(s)
      Yotsutani Naoto
    • Organizer
      金沢トポロジーセミナー
    • Related Report
      2023 Annual Research Report
  • [Presentation] Differential geometric global smoothings of SNC complex surfaces with trivial canonical bundle2023

    • Author(s)
      Yotsutani Naoto
    • Organizer
      東北大学幾何学セミナー
    • Related Report
      2023 Annual Research Report
    • Invited
  • [Presentation] Strong Calabi dream structure of Bott manifolds2023

    • Author(s)
      四ッ谷直仁
    • Organizer
      Toric Topology 2023 in Osaka
    • Related Report
      2022 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Diffeomorphism classes of the doubling Calabi-Yau threefolds2022

    • Author(s)
      四ッ谷直仁
    • Organizer
      2023年度日本数学会秋季総合分科会(北海道大学)
    • Related Report
      2022 Research-status Report
  • [Presentation] 自明な標準束をもつ単純正規交叉複素曲面の微分幾何学的大域スムージングの応用について2022

    • Author(s)
      四ッ谷直仁
    • Organizer
      2023年度日本数学会秋季総合分科会(北海道大学)
    • Related Report
      2022 Research-status Report
  • [Presentation] 自明な標準束をもつ単純正規交叉複素曲面の微分幾何学的大域スムージングについて2022

    • Author(s)
      四ッ谷直仁
    • Organizer
      専門家向け勉強会「ケーラー多様体上の標準計量とその周辺3」
    • Related Report
      2022 Research-status Report
  • [Presentation] Diffeomorphism classes of the doubling Calabi-Yau threefolds2022

    • Author(s)
      四ッ谷直仁
    • Organizer
      2022年度日本数学会年会(埼玉大学)
    • Related Report
      2021 Research-status Report
  • [Presentation] Diffeomorphism classes of the doubling Calabi-Yau threefolds2021

    • Author(s)
      四ッ谷直仁
    • Organizer
      可微分写像の特異点論及びその応用
    • Related Report
      2021 Research-status Report
  • [Presentation] Global smoothings of degenerate K3 surfaces with triple points2020

    • Author(s)
      Naoto Yotsutani
    • Organizer
      The 26th Symposium on Complex geometry
    • Related Report
      2020 Research-status Report
    • Invited
  • [Presentation] Global smoothings of degenerate K3 surfaces with triple points2020

    • Author(s)
      Naoto Yotsutani
    • Organizer
      城崎代数幾何シンポジウム2020
    • Related Report
      2020 Research-status Report
    • Invited
  • [Presentation] Bott-Chern Classes and GIT-stability2020

    • Author(s)
      Naoto Yotsutani
    • Organizer
      ケーラー多様体上の標準軽量とその周辺
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] Diffeomorphic classes of the doubling Caleb-Yau threefolds2020

    • Author(s)
      Naoto Yotsutani
    • Organizer
      Geometry Seminar at Tongji University
    • Related Report
      2019 Research-status Report
  • [Presentation] Diffeomorphic classes of the doubling Caleb-Yau threefolds2020

    • Author(s)
      Naoto Yotsutani
    • Organizer
      Topology seminar at Fudan University
    • Related Report
      2019 Research-status Report
  • [Presentation] Diffeomorphic classes of the doubling Caleb-Yau threefolds2020

    • Author(s)
      Naoto Yotsutani
    • Organizer
      Geometry Seminar at Shanghai Tech University
    • Related Report
      2019 Research-status Report
  • [Presentation] The Delta invariant and the various GIT-stability notions of toric Fano varieties2019

    • Author(s)
      Naoto Yotsutani
    • Organizer
      ファノ多様体及び関連する代数幾何学
    • Related Report
      2019 Research-status Report
    • Invited
  • [Presentation] On Uniform K-stability of pairs for algebraic curves2019

    • Author(s)
      Naoto Yotsutani
    • Organizer
      Geometric Analysis seminar at Peking University
    • Related Report
      2019 Research-status Report
  • [Presentation] On uniform K-stability of pairs for complex vector bundles2019

    • Author(s)
      Naoto Yotsutani
    • Organizer
      北九州幾何学研究集会 2019
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] The Loewy filtration and automorphism groups of toric varieties2018

    • Author(s)
      Naoto Yotsutani
    • Organizer
      RIMS Conference:Geometry, Algebra and Combinatorics in Transformation group theory
    • Related Report
      2018 Research-status Report
    • Invited
  • [Presentation] Geometric Invariants and singularities from the viewpoint of cscK metrics2018

    • Author(s)
      Naoto Yotsutani
    • Organizer
      RIMS Workshop:Research on topology and differential geometry using singularity theory of differentiable maps
    • Related Report
      2018 Research-status Report
    • Int'l Joint Research
  • [Presentation] A New notion GIT-stability: Uniform K-stability of pairs2018

    • Author(s)
      Naoto Yotsutani
    • Organizer
      Journal Club in Kahler Geometry @ Fukuoka I
    • Related Report
      2018 Research-status Report
  • [Presentation] On uniform K-stability of pairs for algebraic curves2018

    • Author(s)
      Naoto Yotsutani
    • Organizer
      Journal Club in Kahler Geometry @ Fukuoka II
    • Related Report
      2018 Research-status Report
  • [Remarks] https://researchmap.jp/naoto_yotsutani?lang=en

    • Related Report
      2023 Annual Research Report

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Published: 2018-04-23   Modified: 2025-01-30  

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