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A study on dynamical system for a torus and cohomology

Research Project

Project/Area Number 12640183
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Basic analysis
Research InstitutionKYUSHU UNIVERSITY

Principal Investigator

KAZAMA Hideaki  Faculty of Math. Prof., 数理学研究院, 教授 (10037252)

Co-Investigator(Kenkyū-buntansha) CHOU Kanji  Faculty of Math. Associate Prof., 数理学研究院, 助教授 (10197634)
FURUSHIMA Mikio  Kumamoto Univ. Faculty of Science, Prof., 理学部, 教授 (00165482)
KANEKO Shouichi  Ryukyu Univ. Faculty of Science, Prof., 理学部, 教授 (10194911)
Project Period (FY) 2000 – 2002
Project Status Completed (Fiscal Year 2002)
Budget Amount *help
¥3,300,000 (Direct Cost: ¥3,300,000)
Fiscal Year 2002: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2001: ¥900,000 (Direct Cost: ¥900,000)
Fiscal Year 2000: ¥1,500,000 (Direct Cost: ¥1,500,000)
Keywordsline bundle / Kodaira's lemma / toroidal group / 複素トーラス / 力学系 / 解析的コモホロジー群 / 擬アーベル多様体 / 線形化可能性 / 連分数展開 / 解析的コホモロジー群 / コホモロジーの非ハウスドルフ性 / 擬凸性
Research Abstract

(I) It is a problem whether one can embed a weakly 1-complete manifold with a positive line bundles into a projective space by sections of higher tensor power positive line bundles, or not. It is a very interesting result that one can embed a weakly 1-complete manifold with a positive line bundle by sections of adjoint line bundles instead of the original line bundle by Shigeharu Takayama. This result is proved by a similar method in case of compact manifolds. We apply this method by adjoint line bundle to a problem of line bundle convexity. We get some global result with respect to line bundle convexity of weakly 1-complete manifolds.
(ii) Recently we find an example that Kodaira's lemma does not hold for some strongly 1-complete manifold. Now we try to characterize strongly 1-complete manifolds on which Kodaira's lemma holds alway.
(iii) On troidal groups of cohomologically finite type we can apply the theory of compact Kaehler manifolds. For instance we can show the Hodge decomposition theorem for toroidal groups of cohomologically finite type. We are getting some result for them similar to the results of compact Kaehler manifolds.

Report

(4 results)
  • 2002 Annual Research Report   Final Research Report Summary
  • 2001 Annual Research Report
  • 2000 Annual Research Report

Research Products

(13 results)

All Other

All Publications

  • [Publications] Hideaki KAZAMA: "Nonlinearizability, non-Hausdorff cohomology and neighborhood structure of elliptic curves"Complan Analysis and Related topics in Mathematics 2001. 67-74 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Jyoichi KANEKO: "Classification of Pfaffian systems of Fuchs type of a particular class"Kumamoto J. Math.. 15. 17-52 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Mikio FURUSHIMA: "On the meromorphic convexity of normality domains in a Stein manifold"Manuscripta Math.. 103. 447-453 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Koji Cho: "Characterizations of projective space and applications to complex symplectic manifolds"Adv. Stud. Pure Math.. 35. 1-88 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Hideaki Kazama: "Nonlinearizability non-Hausdorff cohomology and neighborhood structure of elliptic curves"Complex Analysis and Related Topics in Mathematics, 2001. 67-74 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Jyouichi Kaneko: "Classification of Pfaffian systems of Fuchs type of a particular class"Kumamoto J. Math. 15. 17-52 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Mikio Furushima: "On the meromorphic convexity of normality domains in a Stein manifold"Manuscripta Math.. 103. 447-453 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Koji Cho: "Characterizations of projective space and applications to complex symplectic manifolds"Adv. Stud. Pure Math.. 35. 1-88 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2002 Final Research Report Summary
  • [Publications] Hideaki KAZAMA, Kyungnam KIM: "Nonlinearizability and Non-Hocus dorff cohom. and neighborhood structure of elliptic curves"Complex Analysis and Related Topics. 67-75 (2002)

    • Related Report
      2002 Annual Research Report
  • [Publications] Hideaki Kazawa, Kyung Nam Kim: "Nonlinearizability and non-Hausdorff cohomology and neighborhood structure of elliptic curves"Complex Analysis and Related Topics, The Proceedings of the Japan-Korea Joint Workshop in Mathematics. 67-75 (2002)

    • Related Report
      2001 Annual Research Report
  • [Publications] Kazama,H.,Kim,D.K.and C.Y.Oh: "Some remarks on complex Lie groups"Nagoya Math.J.. 157. 47-57 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Kazama,H.and Takayama,S.: "On the dd'-equation over pseudoconvex Kaehler manifolds"Manuscripta Math., Springer Verlag. 102. 25-39 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Kaneko,J.: "On Forrester's generalization of Morris constant term identity"Contemporary Math., American Mathematical Society. 254. 271-282 (2000)

    • Related Report
      2000 Annual Research Report

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Published: 2000-03-31   Modified: 2016-04-21  

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