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Computational complex analysis and algebraic analysis of singularities

Research Project

Project/Area Number 15K04891
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Basic analysis
Research InstitutionUniversity of Tsukuba

Principal Investigator

Tajima Shinichi  筑波大学, 数理物質系, 教授 (70155076)

Co-Investigator(Kenkyū-buntansha) 福井 敏純  埼玉大学, 理工学研究科, 教授 (90218892)
山崎 晋  日本大学, 理工学部, 教授 (00349953)
鍋島 克輔  徳島大学, 大学院社会産業理工学研究部(理工学域), 准教授 (00572629)
Co-Investigator(Renkei-kenkyūsha) Oaku Toshinori  東京女子大学, 現代教養学部, 教授 (60152039)
Shibuta Takafumi  九州産業大学, 理工学部, 講師 (40648200)
Research Collaborator Umeta Yoko  山口大学, 創成科学研究科, 助教 (90606386)
Project Period (FY) 2015-04-01 – 2018-03-31
Project Status Completed (Fiscal Year 2017)
Budget Amount *help
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2017: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥1,950,000 (Direct Cost: ¥1,500,000、Indirect Cost: ¥450,000)
Keywords複素解析 / 代数解析 / 特異点 / アルゴリズム / D-加群 / 局所コホモロジー / スタンダード基底 / integral number / ホロノミーD-加群 / Le numbers / b-関数 / 対数的ベクトル場
Outline of Final Research Achievements

Based on the theory of algebraic analysis and computer algebra, complex analytic aspects of singularities are considered. Main results of our study are (i) an extended ideal membership algorithm in a ring of convergent power series. (ii) algorithms for computing integral numbers, and generalized integral dependence relations of an ideal in a local ring, (iii) algorithms for computing logarithmic vector fields and Bruce-Roberts Milnor numbers, (iv) an algorithm for computing b-functions and relevant holonomic D-modules associated to a hypersurface, (v) an algorithm for computing generic Le numbers.

Report

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

    (70 results)

All 2018 2017 2016 2015

All Journal Article (18 results) (of which Open Access: 12 results,  Peer Reviewed: 10 results,  Acknowledgement Compliant: 2 results) Presentation (52 results) (of which Int'l Joint Research: 8 results,  Invited: 7 results)

  • [Journal Article] グレブナ基底を用いた収束冪級数環での拡張イデアル所属アルゴリズムについて2018

    • Author(s)
      鍋島克輔, 田島慎一
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 2054 Pages: 118-125

    • Related Report
      2017 Annual Research Report
    • Open Access
  • [Journal Article] Comprehensive Groebner systems approach to b-functions of \mu-constant deformations2018

    • Author(s)
      K. Nabeshima, S. Tajima
    • Journal Title

      Saitama Journal of Mathematics

      Volume: 31 Pages: 115-136

    • Related Report
      2017 Annual Research Report
    • Peer Reviewed
  • [Journal Article] Algebraic local cohomology with parameters and parametric standard bases for zero-dimensional ideals2017

    • Author(s)
      Katsusuke Nabeshima, Shinichi Tajima
    • Journal Title

      Journal of Symbolic Computation

      Volume: 82 Pages: 91-122

    • DOI

      10.1016/j.jsc.2017.01.003

    • Related Report
      2017 Annual Research Report 2016 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] 代数的局所コホモロジーを用いた limiting tangent space の計算法と比較2017

    • Author(s)
      鍋島克輔, 田島慎一
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 2019 Pages: 53-63

    • Related Report
      2017 Annual Research Report
    • Open Access
  • [Journal Article] Computer algebra and Bruce-Roberts-Milnor number2017

    • Author(s)
      伊澤毅, 鍋島克輔, 田島慎一
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 2019 Pages: 64-79

    • Related Report
      2017 Annual Research Report 2016 Research-status Report
    • Open Access
  • [Journal Article] Computing mu*-sequences of hypersurface isolated singularities via parametric local cohomology systems2017

    • Author(s)
      K. Nabeshima, S. Tajima,
    • Journal Title

      Acta Mathematica Vietnamica

      Volume: 42 Issue: 2 Pages: 279-288

    • DOI

      10.1007/s40306-016-0198-4

    • Related Report
      2017 Annual Research Report 2016 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Comprehensive Groebner systems approach to b-functions of mu-constant deformations2017

    • Author(s)
      K. Nabeshima, S. Tajima
    • Journal Title

      Saitama Journal of Mathematics

      Volume: 31 Pages: 1-12

    • Related Report
      2016 Research-status Report
    • Peer Reviewed
  • [Journal Article] 代数的局所コホモロジーを用いた Limiting Tangent Spaceの計算法と比較2017

    • Author(s)
      鍋島克輔, 田島慎一
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 2019 Pages: 53-63

    • Related Report
      2016 Research-status Report
    • Open Access
  • [Journal Article] Computing Tjurina stratifications of μ-constant deformations via parametric local cohomology systems2016

    • Author(s)
      Katsusuke Nabeshima, Shinichi Tajima
    • Journal Title

      Applicable Algebra in Engineering, Communication and Computing

      Volume: - Issue: 6 Pages: 451-467

    • DOI

      10.1007/s00200-016-0289-4

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access / Acknowledgement Compliant
  • [Journal Article] Computing structure of holonomic D-modules associated with a simple line singularity2016

    • Author(s)
      S. Tajima, Y. Umeta
    • Journal Title

      RIMS K\^oky\^uroku Bessatsu

      Volume: 57 Pages: 125-140

    • Related Report
      2016 Research-status Report
    • Peer Reviewed
  • [Journal Article] Solving extended ideal membership problems in rings of convergent power series via Grebner bases,2016

    • Author(s)
      K. Nabeshima, S. Tajima
    • Journal Title

      Lecture Notes in Computer Sciences

      Volume: 9582 Pages: 252-267

    • Related Report
      2016 Research-status Report
    • Peer Reviewed / Open Access
  • [Journal Article] Bruce-Roberts ミルナー数の計算アルゴリズム2015

    • Author(s)
      田島慎一, 鍋島克輔
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 1976

    • Related Report
      2015 Research-status Report
    • Open Access
  • [Journal Article] 偏微分作用素環での包括的グレブナー基底系とホロノミーD-加群, b-関数2015

    • Author(s)
      鍋島克輔, 田島慎一
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 1976

    • Related Report
      2015 Research-status Report
    • Open Access
  • [Journal Article] 代数的局所コホモロジーを用いたパラメータ付き拡張ideal membership アルゴリズム2015

    • Author(s)
      鍋島克輔, 田島慎一
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 1955

    • Related Report
      2015 Research-status Report
    • Open Access
  • [Journal Article] 孤立特異点変形と f^s のパラメータ付き偏微分作用素環での annihilator について2015

    • Author(s)
      加藤満生, 田島慎一
    • Journal Title

      京都大学数理解析研究所講究録

      Volume: 1955

    • Related Report
      2015 Research-status Report
    • Open Access
  • [Journal Article] Efficient computation of algebraic local cohomology classes and change of ordering for zero-dimensional standard bases2015

    • Author(s)
      K. Nabeshima and S. Tajima
    • Journal Title

      Lecture Notes in Computer Science

      Volume: 9301

    • Related Report
      2015 Research-status Report
    • Peer Reviewed
  • [Journal Article] Computing logarithmic vector fields associated with parametric semi-quasihomogeneous hypersurface isolated singularities2015

    • Author(s)
      K. Nabeshima and S. Tajima
    • Journal Title

      Proceedings of the International Symposium on Symbolic and Algebraic Computation

      Volume: 2015 Pages: 291-298

    • DOI

      10.1145/2755996.2756641

    • Related Report
      2015 Research-status Report
    • Peer Reviewed
  • [Journal Article] On the computation of algebraic local cohomology classes associated with semi-quasihomogeneous singularities2015

    • Author(s)
      K. Nabeshima and S. Tajima
    • Journal Title

      Advanced Studies in Pure Mathematics

      Volume: 66

    • Related Report
      2015 Research-status Report
    • Peer Reviewed
  • [Presentation] 包括的グレブナー基底系を用いた mu-stratification と mu* 列の計算法について2017

    • Author(s)
      鍋島克輔, 田島慎一
    • Organizer
      Risa/Asir Conference
    • Place of Presentation
      金沢大学, 石川県金沢市
    • Year and Date
      2017-03-28
    • Related Report
      2016 Research-status Report
  • [Presentation] マトリス双対を用いた孤立特異点の不変量の計算2017

    • Author(s)
      渋田敬史, 田島慎一
    • Organizer
      日本数学会, 函数論分科会
    • Place of Presentation
      首都大学東京, 東京都八王子市
    • Year and Date
      2017-03-24
    • Related Report
      2016 Research-status Report
  • [Presentation] パラメータ付きBernstein-SatoイデアルとホロノミーD加群の計算2017

    • Author(s)
      鍋島克輔, 田島慎一
    • Organizer
      日本数学会, 函数論分科会
    • Place of Presentation
      首都大学東京, 東京都八王子市
    • Year and Date
      2017-03-24
    • Related Report
      2016 Research-status Report
  • [Presentation] Computation method for mu*-sequences of hypersurface isolated singularities,2017

    • Author(s)
      K. Nabeshima, S. Tajima
    • Organizer
      Topology of Singularity in Hanoi
    • Place of Presentation
      VIASM, Hanoi, Vietnum
    • Year and Date
      2017-02-20
    • Related Report
      2016 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Tangent cone を用いた局所環でのパラメトリックイデアルの次元判定2017

    • Author(s)
      鍋島克輔, 田島慎一
    • Organizer
      数式処理学会合同分科会
    • Place of Presentation
      京都大学産学連携本部 東京サテライトオフィス、東京都中央区
    • Year and Date
      2017-01-21
    • Related Report
      2016 Research-status Report
  • [Presentation] Grothendieck local residues の計算法について2017

    • Author(s)
      田島慎一
    • Organizer
      多変数函数論冬セミナー
    • Related Report
      2017 Annual Research Report
  • [Presentation] ホロノミーD-加群を用いた Grothendieck local residues の計算法について2017

    • Author(s)
      田島慎一
    • Organizer
      Computer Algebra
    • Related Report
      2017 Annual Research Report
  • [Presentation] 収束冪級数環における generalized integral dependence relation の計算法について2017

    • Author(s)
      田島慎一, 鍋島克輔
    • Organizer
      Computer Algebra
    • Related Report
      2017 Annual Research Report
  • [Presentation] Local cohomology and generalized integral depemdemce relations w.r.t ideals in local rings2017

    • Author(s)
      田島慎一
    • Organizer
      第39回可換環論シンポジウム
    • Related Report
      2017 Annual Research Report
  • [Presentation] A method for computing generic L\^e numbers associated with hypersurface non-isolated singularities2017

    • Author(s)
      田島慎一
    • Organizer
      超局所解析と漸近解析
    • Related Report
      2017 Annual Research Report
  • [Presentation] Computing Bruce-Roberts MIlnor numbers2017

    • Author(s)
      K. Nabeshima, S. Tajima
    • Organizer
      Australian-Japanese Workshop on Real and Complex Singularities
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] A new effective algorithm for computing Grothendieck local residues2017

    • Author(s)
      S. Tajima
    • Organizer
      Several Complex Variables
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] Integral dependence relation と半擬斉次孤立特異点のb-関数2017

    • Author(s)
      鍋島克輔, 田島慎一
    • Organizer
      日本数学会
    • Related Report
      2017 Annual Research Report
  • [Presentation] 収束冪級数環でのintegral numberの計算2017

    • Author(s)
      加藤満生, 鍋島克輔, 田島慎一
    • Organizer
      日本数学会
    • Related Report
      2017 Annual Research Report
  • [Presentation] Transformation lawによるGrothendieck local residue の計算2017

    • Author(s)
      田島慎一, 鍋島克輔
    • Organizer
      日本数学会
    • Related Report
      2017 Annual Research Report
  • [Presentation] b-関数の根に付随したホロノミー系の局所コホモロジー解の計算2017

    • Author(s)
      鍋島克輔, 田島慎一
    • Organizer
      数式処理の新たな発展
    • Related Report
      2017 Annual Research Report
  • [Presentation] Local cohomology, Grothendieck local residues and algorithms2017

    • Author(s)
      S. Tajima
    • Organizer
      Workshop on Residues, Dynamics and Hyperfunctions
    • Related Report
      2017 Annual Research Report
    • Invited
  • [Presentation] Computing integral numbers for a parametric ideal in a ring of convergent power series via comprehensive Groebner systems2017

    • Author(s)
      K. Nabeshima, S. Tajima
    • Organizer
      Applications of Computer Algebra
    • Related Report
      2017 Annual Research Report
    • Int'l Joint Research / Invited
  • [Presentation] 収束冪級数環におけるintegral numberの計算法について2017

    • Author(s)
      鍋島克輔, 田島慎一
    • Organizer
      日本数式処理学会
    • Related Report
      2017 Annual Research Report
  • [Presentation] Generic Le numbers の計算アルゴリズムとホロノミーD-加群2017

    • Author(s)
      田島慎一
    • Organizer
      微分幾何学と特異点論の応用
    • Related Report
      2017 Annual Research Report
  • [Presentation] 特異点の計算複素解析-- 留数, Samuel multiplicity, Chern-Schwartz-MacPherson class --2016

    • Author(s)
      田島慎一
    • Organizer
      多変数関数論冬セミナー
    • Place of Presentation
      福岡工業大学, 福岡県福岡市
    • Year and Date
      2016-12-15
    • Related Report
      2016 Research-status Report
  • [Presentation] b-関数の因子チェックを用いたパラメータ付きb-関数の計算2016

    • Author(s)
      鍋島克輔, 田島慎一
    • Organizer
      数式処理とその周辺分野の研究
    • Place of Presentation
      京都大学数理解析研究所, 京都府京都市
    • Year and Date
      2016-12-07
    • Related Report
      2016 Research-status Report
  • [Presentation] Transformation law によるパラメータ付き多変数留数計算アルゴリズム2016

    • Author(s)
      田島慎一, 鍋島克輔
    • Organizer
      数式処理とその周辺分野の研究
    • Place of Presentation
      京都大学数理解析研究所, 京都府京都市
    • Year and Date
      2016-12-07
    • Related Report
      2016 Research-status Report
  • [Presentation] 局所環における Matlis duality を用いた計算法とその応用2016

    • Author(s)
      渋田敬史, 田島慎一
    • Organizer
      数式処理とその周辺分野の研究
    • Place of Presentation
      京都大学数理解析研究所, 京都府京都市
    • Year and Date
      2016-12-07
    • Related Report
      2016 Research-status Report
  • [Presentation] Limiting tangent spaces and local cohomology2016

    • Author(s)
      田島慎一
    • Organizer
      トポロジーとコンピュータ 2016
    • Place of Presentation
      カレッジプラザ秋田, 秋田県秋田市
    • Year and Date
      2016-10-28
    • Related Report
      2016 Research-status Report
  • [Presentation] Local cohomology solutions of holonomic D-modules associated with non-isolated hypersurface singularities2016

    • Author(s)
      田島慎一
    • Organizer
      超局所解析と特異摂動論の新展開
    • Place of Presentation
      京都大学数理解析研究所, 京都府京都市
    • Year and Date
      2016-10-03
    • Related Report
      2016 Research-status Report
  • [Presentation] パラメータ付きホロノミーD-加群とb-関数--mu-constant deformation の場合2016

    • Author(s)
      鍋島克輔, 田島慎一
    • Organizer
      日本数学会関数論分科会
    • Place of Presentation
      関西大学, 大阪府吹田市
    • Year and Date
      2016-09-15
    • Related Report
      2016 Research-status Report
  • [Presentation] 局所コホモロジーを用いた mu*-列の計算法について2016

    • Author(s)
      鍋島克輔, 田島慎一
    • Organizer
      日本数学会関数論分科会
    • Place of Presentation
      関西大学, 大阪府吹田市
    • Year and Date
      2016-09-15
    • Related Report
      2016 Research-status Report
  • [Presentation] Computer algebra and Bruce-Roberts-Milnor numbers2016

    • Author(s)
      伊澤毅, 鍋島克輔, 田島慎一
    • Organizer
      数式処理の新たな発展
    • Place of Presentation
      京都大学数理解析研究所, 京都府京都市
    • Year and Date
      2016-09-07
    • Related Report
      2016 Research-status Report
  • [Presentation] 代数的局所コホモロジーを用いたlimiting tangent space の計算法と比較2016

    • Author(s)
      鍋島克輔, 田島慎一
    • Organizer
      数式処理の新たな発展
    • Place of Presentation
      京都大学数理解析研究所, 京都府京都市
    • Year and Date
      2016-09-07
    • Related Report
      2016 Research-status Report
  • [Presentation] パラメトリック局所コホモロジーを用いた mu* の計算2016

    • Author(s)
      鍋島克輔, 田島慎一
    • Organizer
      日本数式処理学会
    • Place of Presentation
      福岡大学, 福岡県福岡市
    • Year and Date
      2016-06-03
    • Related Report
      2016 Research-status Report
  • [Presentation] Limiting tangent spaces と local cohomology2016

    • Author(s)
      田島慎一, 鍋島克輔
    • Organizer
      日本数学会, 函数論分科会
    • Place of Presentation
      筑波大学, 茨城県つくば市
    • Year and Date
      2016-03-16
    • Related Report
      2015 Research-status Report
  • [Presentation] パラメータ付き対数的ベクトル場と Bruce-Roberts ミルナー数の計算2016

    • Author(s)
      鍋島克輔, 田島慎一
    • Organizer
      日本数学会, 函数論分科会
    • Place of Presentation
      筑波大学, 茨城県つくば市
    • Year and Date
      2016-03-16
    • Related Report
      2015 Research-status Report
  • [Presentation] Holonomic D-modules associated with non-isolated hypersurface singularities and local monodromy structures of local cohomology solutions2016

    • Author(s)
      田島慎一
    • Organizer
      偏微分方程式の諸問題
    • Place of Presentation
      日本大学駿河台キャンパス, 東京都千代田区
    • Year and Date
      2016-03-03
    • Related Report
      2015 Research-status Report
  • [Presentation] 特異点と多変数留数 I2016

    • Author(s)
      田島慎一
    • Organizer
      Encounter with Mathematics 64
    • Place of Presentation
      中央大学理工学部, 東京都文京区
    • Year and Date
      2016-02-20
    • Related Report
      2015 Research-status Report
  • [Presentation] 特異点と多変数留数 II2016

    • Author(s)
      田島慎一
    • Organizer
      Encounter with Mathematics 64
    • Place of Presentation
      中央大学理工学部, 東京都文京区
    • Year and Date
      2016-02-20
    • Related Report
      2015 Research-status Report
  • [Presentation] 非孤立特異点の計算複素解析と代数解析アルゴリズム2016

    • Author(s)
      田島慎一
    • Organizer
      Encounter with Mathematics 64
    • Place of Presentation
      中央大学理工学部, 東京都文京区
    • Year and Date
      2016-02-20
    • Related Report
      2015 Research-status Report
  • [Presentation] 非孤立特異点を持つ複素解析的超曲面とホロノミーD-加群2016

    • Author(s)
      田島慎一
    • Organizer
      接触構造, 特異点, 微分方程式及びその周辺
    • Place of Presentation
      金沢大学サテライトプラザ, 石川県金沢市
    • Year and Date
      2016-01-20
    • Related Report
      2015 Research-status Report
  • [Presentation] D. Siersma の非孤立特異点に付随するD-加群と Poincar\'e-Birkhoff-Witt 代数2015

    • Author(s)
      田島慎一
    • Organizer
      数式処理とその周辺分野の研究
    • Place of Presentation
      京都大学数理解析研究所, 京都府京都市
    • Year and Date
      2015-12-02
    • Related Report
      2015 Research-status Report
  • [Presentation] グレブナー基底を用いた収束べき級数環上での拡張ideal membershipアルゴリズムに ついて2015

    • Author(s)
      鍋島克輔, 田島慎一
    • Organizer
      数式処理とその周辺分野の研究
    • Place of Presentation
      京都大学数理解析研究所, 京都府京都市
    • Year and Date
      2015-12-02
    • Related Report
      2015 Research-status Report
  • [Presentation] Limiting tangent spaces, Teissier sequences $\mu^{\ast}$ and parametric local cohomology2015

    • Author(s)
      S. Tajima
    • Organizer
      Japanese Australian Workshop on Real and Complex Singularities
    • Place of Presentation
      Kagoshima Univ. Kagoshima
    • Year and Date
      2015-11-23
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research / Invited
  • [Presentation] Solving extended ideal membership problems in rings of convergent series via Groebner bases2015

    • Author(s)
      K. Nabeshima and S. Tajima
    • Organizer
      Sixth International Conference on Mathematical Aspects of Computer and Information Sciences
    • Place of Presentation
      Zuse Institute, Berlin, Germany
    • Year and Date
      2015-11-11
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] 特異点の複素解析と局所コホモロジー2015

    • Author(s)
      田島慎一, 鍋島克輔
    • Organizer
      函数論シンポジウム
    • Place of Presentation
      島根大学, 島根県松江市
    • Year and Date
      2015-10-10
    • Related Report
      2015 Research-status Report
    • Invited
  • [Presentation] D. Siersma の vertical monodromy とホロノミーD-加群2015

    • Author(s)
      田島慎一
    • Organizer
      特異点と多様体の幾何学
    • Place of Presentation
      草津セミナーハウス, 群馬県吾妻郡草津町
    • Year and Date
      2015-09-23
    • Related Report
      2015 Research-status Report
  • [Presentation] Efficient computation of algebraic local cohomology classes and change of ordering for zero-dimensional standard bases,2015

    • Author(s)
      K. Nabeshima and S. Tajima
    • Organizer
      Computer Algebra in Scientific Computing
    • Place of Presentation
      Aachen University, Aahen, Germany
    • Year and Date
      2015-09-14
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] 局所コホモロジーを用いたBruce-Roberts ミルナー数の計算法について2015

    • Author(s)
      田島慎一, 鍋島克輔
    • Organizer
      日本数学会函数論分科会
    • Place of Presentation
      京都産業大学, 京都府京都市
    • Year and Date
      2015-09-13
    • Related Report
      2015 Research-status Report
  • [Presentation] Bruce-Roberts ミルナー数の計算アルゴリズム2015

    • Author(s)
      田島慎一, 鍋島克輔
    • Organizer
      数式処理研究の新たな発展
    • Place of Presentation
      京都大学数理解析研究所, 京都府京都市
    • Year and Date
      2015-08-19
    • Related Report
      2015 Research-status Report
  • [Presentation] 偏微分作用素環での包括的グレブナー基底とホロノミーD-加群, b-関数2015

    • Author(s)
      鍋島克輔, 田島慎一
    • Organizer
      数式処理研究の新たな発展
    • Place of Presentation
      京都大学数理解析研究所, 京都府京都市
    • Year and Date
      2015-08-19
    • Related Report
      2015 Research-status Report
  • [Presentation] Computing logarithmic vector fields associated with parametric semi-quasihomogeneous hypersurface isolated singularities2015

    • Author(s)
      K. Nabeshima and S. Tajima
    • Organizer
      Singularities in Generic Geometry and Applications
    • Place of Presentation
      Kobe Univ. 兵庫県神戸市
    • Year and Date
      2015-07-06
    • Related Report
      2015 Research-status Report
    • Int'l Joint Research
  • [Presentation] Simple line singularities の vanishing cycles と付随するホロノミーD-加群の monodromy 構造について2015

    • Author(s)
      田島慎一, 梅田陽子
    • Organizer
      農工大数学セミナー
    • Place of Presentation
      東京農工大学小金井キャンパス, 東京都小金井
    • Year and Date
      2015-06-23
    • Related Report
      2015 Research-status Report
  • [Presentation] Simple line singularities の vanishing cycles sheaf とホロノミーD-加群2015

    • Author(s)
      田島慎一
    • Organizer
      特異点論月曜セミナー
    • Place of Presentation
      日本大学文理学部, 東京都世田谷区
    • Year and Date
      2015-06-15
    • Related Report
      2015 Research-status Report
  • [Presentation] 代数的局所コホモロジーを用いたスタンダード基底の項順序変換について II2015

    • Author(s)
      鍋島克輔, 田島慎一
    • Organizer
      日本数式処理学会
    • Place of Presentation
      筑波大学, 茨城県つくば市
    • Year and Date
      2015-06-05
    • Related Report
      2015 Research-status Report

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Published: 2015-04-16   Modified: 2019-03-29  

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