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Applications of real singularity theory and the homotopy types of spaces of holomorphic maps

Research Project

Project/Area Number 26400083
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Geometry
Research InstitutionThe University of Electro-Communications

Principal Investigator

YAMAGUCHI Kohhei  電気通信大学, 大学院情報理工学研究科, 教授 (00175655)

Co-Investigator(Kenkyū-buntansha) Guest Martin (GUEST Martin)  早稲田大学, 理工学術院, 教授 (10295470)
山田 裕一  電気通信大学, 大学院情報理工学研究科, 教授 (30303019)
島川 和久  岡山大学, 自然科学研究科, 特命教授 (70109081)
大野 真裕  電気通信大学, 大学院情報理工学研究科, 准教授 (70277820)
Project Period (FY) 2014-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥4,420,000 (Direct Cost: ¥3,400,000、Indirect Cost: ¥1,020,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2016: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2015: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2014: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Keywordsホモトピー型 / 正則写像 / 複素多様体 / 実代数的多様体 / トーリック多様体 / 終結式 / 手術 / 実特異点 / 実代数多様体 / 代数幾何学 / チャーン類 / 絡み目 / ホモトピー論 / 実代数幾何学 / ベクトル束 / ホモロジー群 / ホモトピー群 / 圏
Outline of Final Research Achievements

For complex manifolds X and Y (resp. real algebraic varieties X and Y), let Hol(X,Y) (resp. Alg(X,Y)) denote the space of holomorphic maps (resp. algebraic maps represented by polynomials) from X to Y. In this situation, we consider the inclusion map from Hol(X,Y) or Alg(X,Y) into the space Map(X,Y) of all continuous maps from X to Y, and we would like to investigate what dimension this inclusion map approximates the infinite dimensional space Map(X,Y). This problem is called the Atiyah-Jones-Segal conjecture. In particular, in this research we generalize the result of G. Segal concerning to the space of rational functions.

Report

(5 results)
  • 2017 Annual Research Report   Final Research Report ( PDF )
  • 2016 Research-status Report
  • 2015 Research-status Report
  • 2014 Research-status Report
  • Research Products

    (56 results)

All 2018 2017 2016 2015 2014 Other

All Int'l Joint Research (1 results) Journal Article (20 results) (of which Int'l Joint Research: 7 results,  Peer Reviewed: 17 results,  Open Access: 6 results,  Acknowledgement Compliant: 4 results) Presentation (21 results) (of which Invited: 5 results) Book (1 results) Remarks (13 results)

  • [Int'l Joint Research] ワルシャワ大学(ポーランド)

    • Related Report
      2016 Research-status Report
  • [Journal Article] Nef vector bundles on a quadric surface with the first Chern class (2,1)2018

    • Author(s)
      M. Ohno
    • Journal Title

      Advances in Geometry (掲載決定)

      Volume: (未定)

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Homology and cohomology via enriched bifunctors2018

    • Author(s)
      T. Haraguchi and K. Shimakawa
    • Journal Title

      Kyushu J. Math. (掲載決定)

      Volume: (未定)

    • NAID

      130007521547

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The homotopy type of spaces of resultants of bounded multiplicity2017

    • Author(s)
      A. Kozlowski and K. Yamaguchi
    • Journal Title

      Topology and its Appl.

      Volume: 232 Pages: 112-139

    • DOI

      10.1016/j.topol.2017.10.002

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Four-dimensional manifolds constructed by lens space surgeries of distinct types2017

    • Author(s)
      Motoo Tange and Yuichi Yamada
    • Journal Title

      J. of Knot Theory and its Ramifications

      Volume: 26 No.11 Issue: 11 Pages: 1750069-1750069

    • DOI

      10.1142/s0218216517500699

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] A Lie-theoretic description of the solution space of the tt*-Toda equations2017

    • Author(s)
      M.A. Guest and N.-K, Kuo
    • Journal Title

      Math. Physical. Anal. Geom.

      Volume: 20

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed / Int'l Joint Research
  • [Journal Article] Nef vector bundles on a projective space with first Chern class 3 and second Chern class 82017

    • Author(s)
      M. Ohno
    • Journal Title

      Le Mathematiche (catania)

      Volume: 72 Pages: 69-81

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] The homotopy type of spaces of caprime polynomials revisited2017

    • Author(s)
      A. Kozlowski and K. Yamaguchi
    • Journal Title

      Topology and its Applications (to appear)

      Volume: 印刷準備中

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] The homotopy type of spaces of polynomials with bounded multiplicity2017

    • Author(s)
      A. Kozlowski and K. Yamaguchi
    • Journal Title

      Publ. Res. Inst. Math. Sci. Kyoto Univ. (to appear)

      Volume: 印刷準備中

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] The homotopy type of spaces of polynomials with bounded multiplicity2016

    • Author(s)
      A. Kozlowski and K. Yamaguchi
    • Journal Title

      Publ. Res. Inst. Math. Sci. Kyoto Univ.

      Volume: 52-3 Issue: 3 Pages: 297-308

    • DOI

      10.4171/prims/182

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research
  • [Journal Article] Spaces of algebraic maps from real projective spaces to toric varietiies2016

    • Author(s)
      A. Kozlowski, M. Ohno, and K. Yamaguchi
    • Journal Title

      J. Math. Soc. Japan

      Volume: 68-2 Pages: 745-771

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Open Access / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Note on the space of polynomials with bounded multiplicity2015

    • Author(s)
      K. Yamaguchi
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 1968 Pages: 126-129

    • Related Report
      2015 Research-status Report
    • Open Access
  • [Journal Article] Maximal minors of a matrix with linear form entries2015

    • Author(s)
      H. Ito, A. Noma and M. Ohno
    • Journal Title

      Linear Multilinear Algebra

      Volume: 63 Pages: 1599-1606

    • Related Report
      2015 Research-status Report 2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] Isomonodrtomy aspects of the tt* equations of Cecotti and Vafa II: Riemann-Hilbert problem2015

    • Author(s)
      M. A. Guest, A. R. Its and C-S. Lin
    • Journal Title

      Comm. Math. Phys.

      Volume: 336 Pages: 337-380

    • Related Report
      2015 Research-status Report
    • Peer Reviewed / Int'l Joint Research / Acknowledgement Compliant
  • [Journal Article] Spaces of algebraic maps from real projective spaces to toric varieties2015

    • Author(s)
      A. Kozlowski, M. Ohno, K. Yamaguchi
    • Journal Title

      J. Math. Soc. Japan

      Volume: 印刷中

    • NAID

      130006887146

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] The space of maps from a real projective space to a topic variety2014

    • Author(s)
      A. Kozlowski, 大野真裕, 山口耕平
    • Journal Title

      数理解析研究所講究録

      Volume: 1976 Pages: 120-126

    • Related Report
      2014 Research-status Report
    • Open Access
  • [Journal Article] Spaces of equivariant algebraic maps to topic varieties2014

    • Author(s)
      山口耕平
    • Journal Title

      数理解析研究所講究録

      Volume: 1922 Pages: 28-33

    • Related Report
      2014 Research-status Report
    • Open Access
  • [Journal Article] A spectral sequence and nef vector bundles of the first Chern class two on hyper quadrics2014

    • Author(s)
      M. Ohno, H. Terakawa
    • Journal Title

      Ann. Univ. Ferra Sez. VII Sci. Mat.

      Volume: 60 Pages: 397-406

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] Lens space surgeries along certain 2-component links related with Park's rational blow down, and Reidemeister-Turaev torsion2014

    • Author(s)
      T. Kadokami, Y. Yamada
    • Journal Title

      J. Aust. Math. Soc.

      Volume: 96 Pages: 78-126

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] Orbifold quantum D-modules associated to weighted projective spaces2014

    • Author(s)
      M. Guest, zH. Sakai
    • Journal Title

      Comment Math. Helv.

      Volume: 89 Pages: 273-297

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Journal Article] Non linear PDE aspects of the tt* equations of Cecotti and Vafa2014

    • Author(s)
      M. Guest, C. Lin
    • Journal Title

      J. Reine Angew. Math.

      Volume: 689 Pages: 1-32

    • Related Report
      2014 Research-status Report
    • Peer Reviewed
  • [Presentation] The homotopy of spaces of resultants of bounded multiplicity2018

    • Author(s)
      山口耕平
    • Organizer
      研究集会「福岡ホモトピー論セミナー」, 福岡大学セミナーハウス(福岡市中央区)
    • Related Report
      2017 Annual Research Report
  • [Presentation] Spaces of resultants with bounded multiplicity and its real analogues2018

    • Author(s)
      山口耕平
    • Organizer
      研究集会「実特異点論とその応用」, 北海道大学大学院理学研究院(札幌市北区)
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] Spaces of resultants of bounded multiplicity and its related problems2017

    • Author(s)
      山口耕平
    • Organizer
      研究集会「空間の代数的・幾何的モデルとその周辺」, 信州大学理学部(長野県松本市)
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] Exceptional Dehn surgeries along the Mazur link2017

    • Author(s)
      山田裕一
    • Organizer
      日本数学会 秋季総合分科会(山形大学)
    • Related Report
      2017 Annual Research Report
  • [Presentation] 部分的モノイドにラベルをもつ区間の配置空間2017

    • Author(s)
      奥山真吾,島川和久
    • Organizer
      日本数学会2017年度秋季総合分科会(山形大学小白川キャンパス)
    • Related Report
      2017 Annual Research Report
  • [Presentation] Whitney approximation on smooth cell complexes2017

    • Author(s)
      島川和久,,原口忠之
    • Organizer
      第44回変換群論シンポジウム, (福井市フェニックスプラザ)
    • Related Report
      2017 Annual Research Report
  • [Presentation] 部分的モノイドにラベルをもつ区間の配置空間の構成2017

    • Author(s)
      奥山真吾, 島川和久
    • Organizer
      平成28年度日本数学会中国・四国支部例会
    • Place of Presentation
      愛媛大学理学部(愛媛県松山市)
    • Related Report
      2016 Research-status Report
  • [Presentation] Whitney approximation on smooth cell complexes2017

    • Author(s)
      島川和久
    • Organizer
      研究集会「ホモトピー論と特異点論小研究集会」
    • Place of Presentation
      北海道大学理学部(北海道札幌市)
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] 微分空間のホモトピー論について2017

    • Author(s)
      島川和久
    • Organizer
      研究集会「安定ホモトピー論とその周辺」
    • Place of Presentation
      岡山大学理学部(岡山県岡山市)
    • Related Report
      2016 Research-status Report
  • [Presentation] The homotopy of spaces of rational curves on a toric variety2016

    • Author(s)
      A. Kozlowski, 山口耕平
    • Organizer
      研究集会「群作用と位相」
    • Place of Presentation
      城崎健康福祉センター(兵庫県豊岡市)
    • Year and Date
      2016-12-04
    • Related Report
      2016 Research-status Report
  • [Presentation] レゾルタントのホモトピー型と関連する話題について2016

    • Author(s)
      山口耕平
    • Organizer
      京都大学大学院 理学部 数学教室談話会
    • Place of Presentation
      京都大学大学院理学研究科(京都府京都市)
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] Change maker とトーラス結び目のレンズ空間手術2016

    • Author(s)
      山田裕一
    • Organizer
      研究集会「瀬戸内結び目セミナー」
    • Place of Presentation
      大島商船高専(山口県大島郡周防大島町)
    • Related Report
      2016 Research-status Report
    • Invited
  • [Presentation] 射影空間上の第1チャーン類が3のネフなベクトル束について2016

    • Author(s)
      大野真裕
    • Organizer
      研究集会「射影多様体の幾何とその周辺 2016」
    • Place of Presentation
      高知工科大学永国寺キャンパス(高知県香美市)
    • Related Report
      2016 Research-status Report
  • [Presentation] 射影空間上と2次曲面上の第1チャーン類が小さいネフなベクトル束について2016

    • Author(s)
      大野真裕
    • Organizer
      都の西北代数幾何学セミナー
    • Place of Presentation
      早稲田大学 西早稲田キャンパス(東京都新宿区)
    • Related Report
      2016 Research-status Report
  • [Presentation] レンズ空間手術と4次元多様体のKIrby calculus2015

    • Author(s)
      山田裕一
    • Organizer
      東大トポロジー火曜セミナー
    • Place of Presentation
      東京大学大学院数理科学研究科
    • Year and Date
      2015-12-08
    • Related Report
      2015 Research-status Report
  • [Presentation] Exceptional Dehn surgeries along the Mazur link and its application2015

    • Author(s)
      山田裕一
    • Organizer
      研究集会「4次元トポロジー」
    • Place of Presentation
      大阪市立大学理学部数学教室
    • Year and Date
      2015-11-22
    • Related Report
      2015 Research-status Report
  • [Presentation] Four dimensional manifolds constructed by lens space surgeries2015

    • Author(s)
      山田裕一
    • Organizer
      日本数学会秋季総合分科会トポロジー分科会
    • Place of Presentation
      京都産業大学
    • Year and Date
      2015-09-13
    • Related Report
      2015 Research-status Report
  • [Presentation] Segal type fibration sequences and scanning maps2015

    • Author(s)
      山口耕平
    • Organizer
      RIMS研究集会「新しい変換群の幾何」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2015-05-28
    • Related Report
      2015 Research-status Report
  • [Presentation] The homotopy type of the space of rational curves on a toric variety2015

    • Author(s)
      Andrzej Kozlowski, 山口耕平
    • Organizer
      研究集会「ホモトピー論における有限と無限」
    • Place of Presentation
      九州大学西新プラザ
    • Year and Date
      2015-03-20
    • Related Report
      2014 Research-status Report
  • [Presentation] The Atiyah-Jones type problem for the space of holomorphic maps on a certain toric variety2014

    • Author(s)
      山口耕平
    • Organizer
      第41回変換群シンポジウム
    • Place of Presentation
      愛知県蒲郡市蒲郡市民会館
    • Year and Date
      2014-11-13 – 2014-11-14
    • Related Report
      2014 Research-status Report
  • [Presentation] The space of maps to a real toric variety2014

    • Author(s)
      山口耕平
    • Organizer
      京都大学数理解析研究所研究集会「変換群の位相幾何と代数構造」
    • Place of Presentation
      京都大学数理解析研究所
    • Year and Date
      2014-05-26
    • Related Report
      2014 Research-status Report
  • [Book] 理工系基礎数学演習2015

    • Author(s)
      石田晴久、伊東裕也、榎本直也、大野真裕、木田雅成、久藤衡介、田吉隆夫、内藤敏機、山口耕平、山田裕一
    • Total Pages
      232
    • Publisher
      コロナ社
    • Related Report
      2014 Research-status Report
  • [Remarks] 電気通信大学情報理工学研究科教員検索ホームページ

    • URL

      http://kjk.office.uec.ac.jp/Profiles/4/0000339/profile.html

    • Related Report
      2017 Annual Research Report 2015 Research-status Report
  • [Remarks] 電気通信大学情報理工学研究科教員検索ホームページ

    • URL

      http://kjk.office.uec.ac.jp/Profiles/5/0000495/profile.html

    • Related Report
      2017 Annual Research Report
  • [Remarks] 電気通信大学情報理工学研究科教員検索ホームページ

    • URL

      http://kjk.office.uec.ac.jp/Profiles/6/0000506/profile.html

    • Related Report
      2017 Annual Research Report
  • [Remarks] 早稲田大学数学教室ホームページ

    • URL

      http://www.f.waseda.jp/martin/

    • Related Report
      2017 Annual Research Report
  • [Remarks] 電気通信大学情報理工学研究科教員検索ホームページ (山口耕平)

    • URL

      http://kjk.office.uec.ac.jp/Profiles/4/0000339/profile.html

    • Related Report
      2016 Research-status Report
  • [Remarks] 電気通信大学情報理工学研究科教員検索ホームページ (山田裕一)

    • URL

      http://kjk.office.uec.ac.jp/Profiles/5/0000495/profile.html

    • Related Report
      2016 Research-status Report
  • [Remarks] 電気通信大学情報理工学研究科教員検索ホームページ (大野真裕)

    • URL

      http://kjk.office.uec.ac.jp/Profiles/6/0000506/profile.html

    • Related Report
      2016 Research-status Report
  • [Remarks] 早稲田大学理工学術院数学教室ホームページ (Guest Martin)

    • URL

      http://www.f.waseda.jp/martin/

    • Related Report
      2016 Research-status Report
  • [Remarks] 電気通信大学情報理工学研究科教員検索ホームページ

    • URL

      http://kjk.office.uec.ac.jp/Profiles/4/0000506/profile.html

    • Related Report
      2015 Research-status Report
  • [Remarks] 電気通信大学情報理工学研究科教員検索ホームページ

    • URL

      http://kjk.office.uec.ac.jp/Profiles/4/0000495/profile.html

    • Related Report
      2015 Research-status Report
  • [Remarks] 教員情報検索

    • URL

      http://kjk.office.uec.ac.jp/Profiles/4/0000339/profile.html

    • Related Report
      2014 Research-status Report
  • [Remarks] 教員情報検索

    • URL

      http://kjk.office.uec.ac.jp/Profiles/6/0000506/profile.html

    • Related Report
      2014 Research-status Report
  • [Remarks] 教員情報検索

    • URL

      http://kjk.office.uec.ac.jp/Profiles/5/0000495/profile.html

    • Related Report
      2014 Research-status Report

URL: 

Published: 2014-04-04   Modified: 2019-03-29  

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