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2013 Fiscal Year Annual Research Report

代数幾何と可積分系の融合と深化

Research Project

Project/Area Number 24224001
Research InstitutionKobe University

Principal Investigator

齋藤 政彦  神戸大学, 理学(系)研究科(研究院), 教授 (80183044)

Co-Investigator(Kenkyū-buntansha) 山田 泰彦  神戸大学, 理学(系)研究科(研究院), 教授 (00202383)
太田 泰広  神戸大学, 理学(系)研究科(研究院), 教授 (10213745)
望月 拓郎  京都大学, 数理解析研究所, 教授 (10315971)
吉岡 康太  神戸大学, 理学(系)研究科(研究院), 教授 (40274047)
野海 正俊  神戸大学, 学内共同利用施設等, 教授 (80164672)
Project Period (FY) 2012-05-31 – 2017-03-31
Keywords可積分系 / パンルヴェ方程式 / 相空間 / モジュライ理論 / 量子コホモロジーとミラー対称性 / リーマン・ヒルベルト対応 / 国際研究者交流(フランス、ハンガリー) / 国際情報交換
Research Abstract

齋藤は、F. Lorayと射影曲線上の階数2の安定放物接続のモジュライ空間上で、2方向のラグランジュアンファイブレーションが互いに横断的であることの論文を完成させた.吉岡は、柳田とともにアーベル曲面上のベクトル束やそのBridgeland安定性の構造についてその壁の構造の論文を完成させた. 太田は離散および半離散方程式系の両方に対して、N-ソリトン解を明示的に構成した.望月は、ホロノミックD-加群上のベッチ構造の概念を定義し, その関手性を示すプレプリントを発表した.稲場は確定特異点型の接続のモジュライ空間の構成とリーマン・ヒルベルト対応の記述により、対応するモノドロミー保存変形の微分方程式が幾何学的パンルヴェ性を持つことを一般に示した論文を発表した.
森は3次元の端収縮射の例外集合Cが既約曲線の場合の局所的な分類を完成させた.原岡は多変数完全積分可能系の方程式およびモノドロミー表現のmiddle convolutionを構成した.藤野はコンパクトケーラー多様体の標準環が有限生成であるという基本的結果を得た.細野は高木寛通と、3次元Reye合同に関して現れる2つのカラビ・ヤウ多様体の導来同値性の証明を,グラスマン多様体G(3,6)の古典的な幾何学により与えた.入谷はグロモフ・ウィッテン理論における量子化の構造の研究を進めた.中島は、Bravermanらと共同で4次元ユークリッド空間上のインスタントンのモジュライ空間の交叉コホモロジー群が、W代数の表現の構造を持つことを示した.2013年6月に, 京大数理研で国際研究集会「Development of Moduli theory」を組織し、モジュライ理論の近年の発展について総括を行った.また、2013年9月に研究集会「代数幾何学と可積分系におけるモジュライ理論」を開催し、新しい研究の方向性を探った.

Current Status of Research Progress
Current Status of Research Progress

2: Research has progressed on the whole more than it was originally planned.

Reason

モノドロミー保存変形の幾何学は、齋藤、稲場や海外の共同研究者のF. LorayやS. Szaboらとの共同研究により進みつつある.稲場の確定特異点の論文や、稲場・齋藤の不分岐な不確定特異点の場合の論文の発表により、理論の基礎は確立されたが、さらにモジュライ空間の詳しい構造が明らかになってきており、今後の研究の進展が期待される.また多くの国際研究集会で、招待講演を行っており研究の認知度も上がっている.一方、一般化されたモノドロミー多様体の幾何学的構造や、コホモロジー環の構造の研究が盛んになっており、Cluster代数的な構造、また非可換代数の立場からの研究が国際的に盛んになっており、この方向の研究も進展している.一方、山田らの量子パンルヴェ方程式の研究、離散力学系との関係も明らかになりつつあり大きな進展が望まれる.また、望月は、調和バンドルやツイスターD加群の理論の基礎づけを行い、成果を上げている.また、吉岡のアーベル曲面のベクトル束のモジュライ空間の研究は、Bridgeland安定性との関係から興味深いものである.高次元双有理幾何学においては、森、藤野や共同研究者らが理論を発展させている.また、特命助教で雇用した田中は、正標数での極小モデル理論を構築しようしていて、大きなブレークスルーが期待される.また、数理物理学的研究、ミラー対称性に関する研究も、細野、入谷、戸田らにより進展している.他の連携研究者の研究も進展しており、今後はさらなる研究の進展に向けて情報の共有を進めたい.2014年8月に行われるソウルでの国際数学者会議で研究分担者の望月が総合講演者、戸田が代数幾何分野で招待講演者に推薦された事は、非常に名誉な事である.

Strategy for Future Research Activity

研究代表者、研究分担者、連携研究者はそれぞれの分野で関連する独自の研究を進めるとともに、国際共同研究を進める.微分幾何学との関連を重視し、この分野で、新たに連携研究者を加える.またフランス、ベルギー、台湾、米国等の大学の研究者と国際的情報交換を行い、研究の進展を促す.

  • Research Products

    (67 results)

All 2014 2013 Other

All Journal Article (25 results) (of which Peer Reviewed: 23 results) Presentation (39 results) (of which Invited: 39 results) Book (1 results) Remarks (2 results)

  • [Journal Article] Lagrangian Fibrations in Duality on Moduli Spaces of Rank 2 Logarithmic Connections Over the Projective Line2014

    • Author(s)
      F. Loray, M-H. Saito
    • Journal Title

      International Mathematics Research Notices

      Volume: 掲載確定 Pages: 掲載確定

    • DOI

      10.1093/imrn/rnt232

    • Peer Reviewed
  • [Journal Article] Bridgeland's stabilities on abelian surfaces2014

    • Author(s)
      S. Yanagida, K. Yoshioka
    • Journal Title

      Mathematische Zeitschrift

      Volume: 276, No.1-2 Pages: 571-610

    • DOI

      10.1007/s00209-013-1214-1

    • Peer Reviewed
  • [Journal Article] Multi-Poly-Bernoulli Numbers and Finite Multiple Zeta Valuess2014

    • Author(s)
      M. Kaneko, K. Imatomi, E. Takeda
    • Journal Title

      Journal of Integer Sequences

      Volume: 17 Pages: -

  • [Journal Article] Some remarks on the semipositivity theorems2014

    • Author(s)
      O. Fujino, T. Fujisawa, M. Saito
    • Journal Title

      Publications of the Research Institute for Mathematical Sciences

      Volume: 50 Pages: 85--112

    • DOI

      10.4171/PRIMS/125

    • Peer Reviewed
  • [Journal Article] On almost holomorphic Lagrangian fibrations2014

    • Author(s)
      D. Matsushita
    • Journal Title

      Mathematische Annalen

      Volume: 358 Pages: 565--572

    • DOI

      10.1007/s00208-013-0964-8

    • Peer Reviewed
  • [Journal Article] Cluster algebras and singular supports of perverse sheaves2014

    • Author(s)
      H. Nakajima
    • Journal Title

      Advances in Representation Theory of Algebras EMS Series of Congress Reports

      Volume: - Pages: 211-230

    • DOI

      10.4171/125-1/7

    • Peer Reviewed
  • [Journal Article] An error estimate for counting S_3-sextic number fields2014

    • Author(s)
      T. Taniguchi, F. Thorne
    • Journal Title

      International Journal of Number Theory

      Volume: 掲載確定 Pages: 掲載確定

    • DOI

      10.1142/S1793042114500080

    • Peer Reviewed
  • [Journal Article] Semi-homogeneous sheaves, Fourier-Mukai transforms and moduli of stable sheaves on Abelian surfaces2013

    • Author(s)
      S. Yanagida, K. Yoshioka
    • Journal Title

      Journal fur die reine und angewandte Mathematik

      Volume: 684 Pages: 31--86

    • DOI

      10.1515/crelle-2011-0010

    • Peer Reviewed
  • [Journal Article] Integrable Discretizations of the Dym Equation2013

    • Author(s)
      B.-F. Feng, J. Inoguchi, K. Kajiwara, K. Maruno and Y.Ohta
    • Journal Title

      Frontiers of Mathematics in China

      Volume: 8 Pages: 1017-1029

    • DOI

      10.1007/s11464-013-0321-y

    • Peer Reviewed
  • [Journal Article] グレブナー基底候補の正当性検証について2013

    • Author(s)
      M. Noro, K. Yokoyama
    • Journal Title

      数理解析研究所講究録

      Volume: 1843 Pages: 38--50

  • [Journal Article] On the Borel summability of 0-parameter solutions of nonlinear ordinary differential equations2013

    • Author(s)
      S. Kamimoto, T. Koike
    • Journal Title

      Kokyuroku Bessatsu

      Volume: B40 Pages: 191--212

    • Peer Reviewed
  • [Journal Article] Exact WKB analysis of second-order non-homogeneous linear ordinary differential equations2013

    • Author(s)
      T. Koike, Y. Takei
    • Journal Title

      Kokyuroku Bessatsu

      Volume: B40 Pages: 293--313

    • Peer Reviewed
  • [Journal Article] Moduli of parabolic connections on curves and the Riemann-Hilbert correspondence2013

    • Author(s)
      M-a. Inaba
    • Journal Title

      The Journal of Algebraic Geometry

      Volume: 22 No.3 Pages: 407--480

    • DOI

      10.1090/S1056-3911-2013-00621-9

    • Peer Reviewed
  • [Journal Article] The Ramanujan-Serre differential operators and certain elliptic curves2013

    • Author(s)
      M. Kaneko Y. Sakai
    • Journal Title

      The Ramanujan-Serre differential operators and certain elliptic curves

      Volume: 141 (10) Pages: 3421--3429

    • Peer Reviewed
  • [Journal Article] Double zeta values, double Eisenstein series, and modular forms of level 22013

    • Author(s)
      M. Kaneko, K. Tasaka, E. Takeda
    • Journal Title

      Mathematische Annalen

      Volume: 367 Pages: 1091--1118

    • DOI

      10.1007/s00208-013-0930-5

    • Peer Reviewed
  • [Journal Article] Prolongability of ordinary differential equations2013

    • Author(s)
      Y. Haraoka
    • Journal Title

      Journal of Nonlinear Mathematical Physics

      Volume: 20 Pages: 70--84

    • DOI

      10.1080/14029251.2013.862435

    • Peer Reviewed
  • [Journal Article] On the ACC for lengths of extremal rays2013

    • Author(s)
      O. Fujino, Y. Ishitsuka
    • Journal Title

      Tohoku Mathematical Journal(2)

      Volume: 65 Pages: 93--103

    • DOI

      10.2748/tmj/1365452627

    • Peer Reviewed
  • [Journal Article] On the F-purity of isolated log canonical singularities2013

    • Author(s)
      O. Fujino, S. Takagi
    • Journal Title

      Compositio Mathematica

      Volume: 149 Pages: 1495--1510

    • DOI

      10.1112/S0010437X1300715X

    • Peer Reviewed
  • [Journal Article] A transcendental approach to Kollar's injectivity theorem II2013

    • Author(s)
      O. Fujino
    • Journal Title

      Journal fur die reine und angewandte Mathematik

      Volume: 681 Pages: 149--174

    • DOI

      10.1515/crelle-2012-0036

    • Peer Reviewed
  • [Journal Article] Zariski decomposition and Lagrangian fibration on HyperKahler manifolds2013

    • Author(s)
      D. Matsushita, D-Q. Zhang
    • Journal Title

      Mathematical Research Letters

      Volume: 20, No. 5 Pages: 1--9

    • Peer Reviewed
  • [Journal Article] Landau-Ginzburg/Calabi-Yau correspondence, global mirror symmetry and Orlov equivalence2013

    • Author(s)
      A. Chiodo, H. Iritani, Y. Ruan
    • Journal Title

      Publications mathematiques de l'IHES

      Volume: 掲載確定 Pages: 掲載確定

    • DOI

      10.1007/s10240-013-0056-z

    • Peer Reviewed
  • [Journal Article] Secondary terms in counting functions for cubic fields2013

    • Author(s)
      T. Taniguchi, F. Thorne
    • Journal Title

      Duke Mathematical Journal

      Volume: 163 Pages: 2451--2508

    • DOI

      10.1215/00127094-2371752

    • Peer Reviewed
  • [Journal Article] Orbital L-functions for the space of binary cubic forms2013

    • Author(s)
      T. Taniguchi, F. Thorne
    • Journal Title

      Canadian Journal of Mathematics

      Volume: 65 Pages: 1320--1383

    • DOI

      10.4153/CJM-2013-027-0

    • Peer Reviewed
  • [Journal Article] Displacement of polydisks and Lagrangian Floer thoery2013

    • Author(s)
      K. Fukaya, Y.-G. Oh, H. Ohta and K.Ono
    • Journal Title

      Journal of Symplectic Geometry

      Volume: 11 Pages: 231--268

    • DOI

      10.4310/JSG.2013.v11.n2.a4

    • Peer Reviewed
  • [Journal Article] Lagrangian Floer theory over integers: spherically positive symplectic manifolds2013

    • Author(s)
      K. Fukaya, Y.-G. Oh, H. Ohta and K. Ono
    • Journal Title

      Pure and Applied Mathematics Quarterly (Special Issue dedicated to Professor Dennis Sullivan)

      Volume: 9 Pages: 189--289

    • DOI

      10.4310/PAMQ.2013.v9.n2.a1

    • Peer Reviewed
  • [Presentation] Affine Weyl groups, Painlev'e equations and special functions (I), (II)2014

    • Author(s)
      M. Noumi
    • Organizer
      The 6th TIMS-OCAMI-WASEDA Joint International Workshop on Integrable Systems and Mathematical Physics
    • Place of Presentation
      National Taiwan University (taipei, 台湾)
    • Year and Date
      20140323-20140324
    • Invited
  • [Presentation] On the geometry of isomonodromic differential equations (I), (II)2014

    • Author(s)
      M-H. Saito
    • Organizer
      The 6th TIMS-OCAMI-WASEDA Joint International Workshop on Integrable Systems and Mathematical Physics
    • Place of Presentation
      National Taiwan University (taipei, 台湾)
    • Year and Date
      20140322-20140323
    • Invited
  • [Presentation] Instanton and representation theory2013

    • Author(s)
      H. Nakajima
    • Organizer
      The 6th MSJ-SI -- Development of Moduli Theory
    • Place of Presentation
      京都大学数理解析研究所 (京都)
    • Year and Date
      20130611-20130614
    • Invited
  • [Presentation] 3 Lectures on Compactification of the moduli space of abelian varieties2013

    • Author(s)
      I. Nakamura
    • Organizer
      The 6th MSJ-SI Development of Moduli Theory (Lecture Series)
    • Place of Presentation
      京都大学数理解析研究所(京都)
    • Year and Date
      20130611-20130613
    • Invited
  • [Presentation] Lectures on Lagrangian Floer theory (five 2.5 hour lectures)2013

    • Author(s)
      K. Ono
    • Organizer
      Advanced Seminar Series on "Symplectic Geometry and Topological Field Theory"
    • Place of Presentation
      Beijing International Center for Mathematical Research (Beijing, China)
    • Year and Date
      20130513-20130517
    • Invited
  • [Presentation] Lagrangian fibration in duality on moduli space of rank two logarithmic connections over the projective line (joint work with F. Loray)

    • Author(s)
      M-H. Saito
    • Organizer
      Algebraic Geometry and Differential Topology Seminar
    • Place of Presentation
      Alfred Renyi Institute of Mathematics (Budapest, Hungary)
    • Invited
  • [Presentation] Lagrangian fibrations in duality on moduli space of logarithmic connections over a curve (joint works with Frank Loray)

    • Author(s)
      M-H. Saito
    • Organizer
      Moduli theory in Algebraic geometry and Integrable systems
    • Place of Presentation
      京都大学数理解析研究所 (京都)
    • Invited
  • [Presentation] Apparent singularities and canonical coordinates for the moduli spaces of singular connections (a joint work with S. Szabo)

    • Author(s)
      M-H. Saito
    • Organizer
      Symplectic Algebraic Geometry
    • Place of Presentation
      関西セミナーハウス(京都)
    • Invited
  • [Presentation] Painlevé property for isomonodromic equations; Algebraic construction of the phase spaces and the Riemann-Hilbert correspondence

    • Author(s)
      M-H. Saito
    • Organizer
      Recent progress in the theory of Painleve equations: algebraic, asymptotic and topological aspects
    • Place of Presentation
      IRMA (Strasbourg, France)
    • Invited
  • [Presentation] Bridgeland stability and stable sheaves on abelian surfaces

    • Author(s)
      K. Yoshioka
    • Organizer
      The 6th MSJ-SI -- Development of Moduli Theory
    • Place of Presentation
      京都大学数理解析研究所 (京都)
    • Invited
  • [Presentation] Bridgeland stability on abelian surfaces

    • Author(s)
      K. Yoshioka
    • Organizer
      Workshop on Geometric Correspondences of Gauge Theories
    • Place of Presentation
      ICTP (Trieste, Italy)
    • Invited
  • [Presentation] 空間離散曲線の等周変形と離散K曲面

    • Author(s)
      井ノ口 順一, 梶原 健司, 松浦 望, 太田 泰広
    • Organizer
      平成25年度九州大学応用力学研究所共同利用研究集会「非線形波動研究の拡がり」
    • Place of Presentation
      九州大学 (福岡)
    • Invited
  • [Presentation] Nahm transforms for harmonic bundles

    • Author(s)
      T. Mochizuki
    • Organizer
      The 6th MSJ-SI -- Development of Moduli Theory
    • Place of Presentation
      京都大学数理解析研究所 (京都)
    • Invited
  • [Presentation] Wild harmonic bundles and some applications

    • Author(s)
      T. Mochizuki
    • Organizer
      The Asian Mathematical Conference 2013
    • Place of Presentation
      Convention Halls in BEXCO (Busan, Korea)
    • Invited
  • [Presentation] グレブナー基底候補の高速生成法とその検証について

    • Author(s)
      野呂 正行
    • Organizer
      RIMS研究集会「数式処理とその周辺分野の研究 -- Computer Algebra and Related Topics」
    • Place of Presentation
      京都大学数理解析研究所 (京都)
    • Invited
  • [Presentation] On irregular modified A-hypergeometric series and Borel summation method

    • Author(s)
      T. Koike
    • Organizer
      Formal and Analytic Solutions of Differential, Difference and Discrete Equations
    • Place of Presentation
      Stefan Banach International MathematicalConference Center (Bedlewo,Porland)
    • Invited
  • [Presentation] On irregular modified A-hypergeometric systems and the Borel summation method

    • Author(s)
      T. Koike
    • Organizer
      Recent progress in the theory of Painlevé equations: algebraic, asymptotic and topological aspects
    • Place of Presentation
      IRMA (Strasbourg, France)
    • Invited
  • [Presentation] Enriques surfaces with 720 symmetries

    • Author(s)
      S. Mukai
    • Organizer
      Lazarsfeld 教授還暦記念代数幾何学研究集会
    • Place of Presentation
      University of Michigan (USA)
    • Invited
  • [Presentation] Enriques surfaces as neighbors of rational surfaces and vice vers

    • Author(s)
      S. Mukai
    • Organizer
      Complex Algebraic Geometry
    • Place of Presentation
      Mathematisches Forschungsinstitut Oberwolfach (Oberwolfach, Germany)
    • Invited
  • [Presentation] Fano 3-folds, moduli and automorphism groups etc.

    • Author(s)
      S. Mukai
    • Organizer
      The 6th MSJ-SI -- Development of Moduli Theory
    • Place of Presentation
      京都大学数理解析研究所(京都)
    • Invited
  • [Presentation] K3, Enriques曲面とルート系について

    • Author(s)
      向井 茂
    • Organizer
      第12回岡シンポジウム
    • Place of Presentation
      奈良女子大学 (奈良)
    • Invited
  • [Presentation] Finite multiple zeta values

    • Author(s)
      M. Kaneko
    • Organizer
      28th Journées Arithmétiques JA2013
    • Place of Presentation
      Fourier Institute Univ. Grenoble (France)
    • Invited
  • [Presentation] Rigidity for holonomic systems in several variables

    • Author(s)
      原岡 喜重
    • Organizer
      Formal and Analytic Solutions of Differential, Difference and Discrete Equations
    • Place of Presentation
      北海道大学理学部 (北海道)
    • Invited
  • [Presentation] On construction of holonomic systems

    • Author(s)
      Y. Haraoka
    • Organizer
      Global Study of Differential Equations in the Complex Domain, Polish-Japanese research group
    • Place of Presentation
      Banach Center (Warsaw, Poland)
    • Invited
  • [Presentation] Rigidity of local systems over complement spaces

    • Author(s)
      Y. Haraoka
    • Organizer
      Moduli theory in Algebraic geometry and Integrable systems
    • Place of Presentation
      京都大学数理解析研究所 (京都)
    • Invited
  • [Presentation] Dimer models and non-commutative crepant resolutions

    • Author(s)
      A. Ishii
    • Organizer
      Noncommutative Algebraic Geometry and Related Topics
    • Place of Presentation
      京都大学数理解析研究所 (京都)
    • Invited
  • [Presentation] Dimer models and non-commutative crepant resolutions

    • Author(s)
      石井 亮
    • Organizer
      代数幾何学城崎シンポジウム
    • Place of Presentation
      兵庫県立城崎大会議館 (兵庫)
    • Invited
  • [Presentation] Some applications of the semi-positivity theorems

    • Author(s)
      O. Fujino
    • Organizer
      Birational geometry of complex algebraic varieties
    • Place of Presentation
      CIRM(Marseille, France)
    • Invited
  • [Presentation] ファノ多様体についてのいくつかの問題

    • Author(s)
      藤野 修
    • Organizer
      Fano多様体の最近の進展
    • Place of Presentation
      京都大学数理解析研究所 (京都)
    • Invited
  • [Presentation] On the dual fibration of a Lagrangian fibration

    • Author(s)
      D. Matsushita
    • Organizer
      Moduli spaces of irreducible symplectic varieties, cubics and Enriques surfaces
    • Place of Presentation
      Laboratoire Paul Painlevé (Lille, France)
    • Invited
  • [Presentation] An example of strange duality for K3 surfaces

    • Author(s)
      K. Abe
    • Organizer
      Moduli theory in Algebraic geometry and Integrable systems
    • Place of Presentation
      京都大学数理解析研究所 (京都)
    • Invited
  • [Presentation] Fock Sheaf of Givental Quantization

    • Author(s)
      H. Iritani
    • Organizer
      Hamiltonian PDEs, Frobenius manifolds and Deligne-Mumford moduli spaces
    • Place of Presentation
      SISSA (Trieste, Italy)
    • Invited
  • [Presentation] Gamma Conjectures for Fano manifolds

    • Author(s)
      H. Iritani
    • Organizer
      Primitive forms and related subjects
    • Place of Presentation
      Kavli IPMU (University of Tokyo, 千葉)
    • Invited
  • [Presentation] Cluster algebras and singular supports of perverse sheaves

    • Author(s)
      H. Nakajima
    • Organizer
      Interactions between Noncommutative Algebra, Representation Theory, and Algebraic Geometry
    • Place of Presentation
      MSRI (Berkeley, USA)
    • Invited
  • [Presentation] The complete moduli spaces of degenerate abelian varieties

    • Author(s)
      I. Nakamura
    • Organizer
      The 6th MSJ-SI Development of Moduli Theory (Conference)
    • Place of Presentation
      京都大学数理解析研究所(京都)
    • Invited
  • [Presentation] Compactification of the moduli space of abelian varieties

    • Author(s)
      I. Nakamura
    • Organizer
      The 6th Pacific RIM Conference on Mathematics 2013
    • Place of Presentation
      Sapporo Convention Center (北海道)
    • Invited
  • [Presentation] Orbital L-functions for the space of binary cubic forms and their applicationas

    • Author(s)
      T. Taniguchi
    • Organizer
      Combinatorics, Multiple Dirichlet series and Analytic Number Theory
    • Place of Presentation
      ICERM (Brown University, USA)
    • Invited
  • [Presentation] Lagrangian Floer theory: the case of toric manifolds

    • Author(s)
      K. Ono
    • Organizer
      Calabi-Yau Geometry and Mirror Symmetry conference
    • Place of Presentation
      Taida Institute for Mathematical Sciences, National Taiwan University (Taipei, Taiwan)
    • Invited
  • [Presentation] Frobenius manifold structure and Lagrangian Floer theory for toric manifolds

    • Author(s)
      K. Ono
    • Organizer
      Primitive forms and related subjects
    • Place of Presentation
      Kavli IPMU (University of Tokyo, 千葉)
    • Invited
  • [Book] Groebner Bases - Statistics and Software Systems 22013

    • Author(s)
      JST/CREST Hibi team (Ed. T. Hibi, Ch. 3, M. Noro)
    • Total Pages
      474頁(107-163)
    • Publisher
      Springer
  • [Remarks] Wellcome to MASA-HIKO SAITO's Home Page

    • URL

      http://www2.kobe-u.ac.jp/~mhsaito/ftop.html

  • [Remarks] 齋藤政彦

    • URL

      http://www2.kobe-u.ac.jp/~mhsaito/ftop-j.html

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Published: 2015-05-28  

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