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1990 Fiscal Year Final Research Report Summary

Algebraic Homology and It's Application

Research Project

Project/Area Number 01540041
Research Category

Grant-in-Aid for General Scientific Research (C)

Allocation TypeSingle-year Grants
Research Field 代数学・幾何学
Research InstitutionKyoto University

Principal Investigator

IWAI Akira  Kyoto University Yoshida College Professor, 教養部, 教授 (70026764)

Co-Investigator(Kenkyū-buntansha) AKIBA Tomoharu  Kyoto University Yoshida College Professor, 教養部, 教授 (60027670)
YOSHINO Yuuji  Kyoto University Yoshida College Assistant Professor, 教養部, 助教授 (00135302)
UE Masaaki  Kyoto University Yoshida College Assistant Professor, 教養部, 助教授 (80134443)
FUJIKI Akira  Kyoto University Yoshida College Assistant Professor, 教養部, 助教授 (80027383)
SAITO Hiroshi  Kyoto University Yoshida College Assistant Professor, 教養部, 助教授 (20025464)
Project Period (FY) 1989 – 1990
KeywordsTwisted conjugacy class / Hasse Principle / Hyperkahler structure / Moment map / Seifert fibered space / Diffeomophism type / Cohen-Macaulay module / Representation of algebras
Research Abstract

In our study we pursued the study of the homology of algebras and related topics. The main results are as follows :
1. Saito proved a Hasse principle on twisted conjugacy classes in the multiplicative group of division algebras, which asserts that the twisted conjugacy classes over an algebraic number field are determined by those over the completions of the number field. 2. Fujiki has shown that on the set of equivalence classes of the representations of the fundamental group of a compact Kahler manifold into a complex reductive algebraic group one can introduce a natural structure of a hyperkahler manifold ; more over, in the corresponding Calabi family the two special fibers are isomorphic, via the Hitchin correspondence, to the moduli space of stable Higgs bundle corresponding to the representations [2]. 3. Ue showed that the diffeomorphism types of the Seifert fibered 4-manifolds over the euclidean base orbifolds are determined by their fundamental groups and gave the correspondence between them and certain four types of geometries [4], and also showed similar results for the cases when the basse orbifolds are not euclidean. He gave the decompositions of simply connected elliptic surfaces as 4-manifolds along some Brieskorn homology spheres concretely in different two way. He also constructed the involutions on the elliptic surfaces which reverse the orientations of the fibers and base apaces. 4. Yoshino determined the Cohen-Macaulay representation type for certain Cohen-Macaulay local rings, and has studied, from the algebraic point of view, the relation between singularities and Cohen-Macualay representation types.

  • Research Products

    (12 results)

All Other

All Publications (12 results)

  • [Publications] 斎藤 裕: "On a Hasse prinCiple for σーConjugacy" G・of Math.Kyoto University. 29. 601-608 (1989)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 藤木 明: "The Noduli Space of Extremal Comract Kahler Manifolds and Generalized WeilーPatersson metrice" Publ.RIMS Kyoto Univ.26. 1-82 (1990)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 上 正明: "Geometric 4ーmanifolds in the seasl of Thusston and Seifent 4ーmanifalds I" J.Math Soc.Japan. 42. 511-540 (1990)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 上 正明: "Geometric 4ーmanifolds in the sease of Thusston and Seifent 4ーmanfolds II" preprint.

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 秋葉 知温: "Remarks on flat and Relatuely Seminormal Pairs" Kobe J.Math.6. 217-222 (1989)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] 吉野 雄二: "CohenーMacaulay Modules over cohenーmachulay Rings" dondon Math SOC.dec.Note.

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] Tomoharu, Akiba: "Remarks on flat and Relatively Seminormal Pairs" Kobe J. Math.v. 6. 217-222 (1989)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Masaaki, Ue: "Geometric 4-manifolds in the sease of Thusston and Seifert 4-manifolds I" J. Math. Soc. Japan. v. 42. (1990)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Masaaki, Ue: "Geometric 4-manifolds in the sease of Thusston and Seifert 4-manifolds II"

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Hiroshi, Saito: "On a Hasse principle for a-conjugacy" J. Math. Kyoto Univ.v. 29. 105-117 (1989)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Akira, Fujiki: "The moduli Space of Extremal Compact Kahler Manifolds and Generalized Weil-Patersson Metrics" Publ. RIMS Kyoto Univ.v. 26. 1-82 (1990)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] Yuuji, Yoshino: "Cohen-Macaulay Modules over Cohen-Machulay Rings" London Math. Sci. Lec. Note.

    • Description
      「研究成果報告書概要(欧文)」より

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Published: 1993-08-12  

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