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A study of three codimensional graded Buchsbaum domains

Research Project

Project/Area Number 12640026
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Algebra
Research InstitutionHiroshima University

Principal Investigator

AMASAKI Mutsumi  Hiroshima University, Graduate School of Education, associate professor, 大学院・教育学研究科, 助教授 (10243536)

Project Period (FY) 2000 – 2001
Project Status Completed (Fiscal Year 2001)
Budget Amount *help
¥1,700,000 (Direct Cost: ¥1,700,000)
Fiscal Year 2001: ¥700,000 (Direct Cost: ¥700,000)
Fiscal Year 2000: ¥1,000,000 (Direct Cost: ¥1,000,000)
Keywordsbasic sequence / groebner basis / generic initial / integral curve / Buchsbaum curve
Research Abstract

1. A computer program has been made that enables us to find the candidates for the system of minimal generators of the generic initial ideal of a three codimensional Cohen-Macaulay homogeneous ideal in a polynomial ring, with the use of its basic sequence. It is useful because the first three parts of the basic sequence of a three codimensional homogeneous ideal defining a graded Buchsbaum ring coincides with the basic sequence of a three codimensional homogeneous ideal defining a graded Cohen-Macaulay ring.
2. We have been trying to construct an integral arithmetically Buchsbaum curve on a nonsingular hypersurface in the four dimensional projective space, with the help of the usual Bourbaki sequence associated with the maximal Buchsbaum graded module obtained by taking the minimal free resolution of the ground field. By our past results, we know all possible basic sequences of arithmetically Buchsbaum curves, but we have not yet been able to check by this method which sequences correspond to integral curves. The difficulty seems to come from the lack of complete knowledge of maximal Cohen-Macaulay modules on R/(f).
3. In order to reconsider the two codimensional case, a lot of our informal results obtained in the past on the basic sequences of integral curves in the three dimensional projective space, have now been written in a paper. Further, applying the above mentioned computer program to this case, we have found that the condition proposed by Cook and the set of conditions described in this paper together make a better set of necessary conditions for the basic sequence of an integral curve in the three dimensional projective space to satisfy.

Report

(3 results)
  • 2001 Annual Research Report   Final Research Report Summary
  • 2000 Annual Research Report
  • Research Products

    (10 results)

All Other

All Publications (10 results)

  • [Publications] Mutsumi Amasaki: "Generic Groebner bases and Weierstrass bases of homogeneous submodules of graded free modules"Journal of Pure and Applied Algebra. 152. 3-16 (2000)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Mutsumi Amasaki: "Homogeneous prime ideals and graded modules fitting into long Bourabaki sequences"Journal of Pure and Applied Algebra. 162. 1-21 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Mutsumi Amasaki: "On the basic sequences of integral curves in P^3"第23回可換環論シンポジウム報告集. 58-67 (2002)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] M. Amasaki: "Generic Groebner bases and Weierstrass bases homogeneous submodules of graded tree modules"Journal of Pure and Applied Algebra. 152. 3-16 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] M. Amasaki: "Homogeneous prime ideals and graded modules fitting into long Bourbaki sequences"Journal of Pure and Applied Algebra. 162. 1-21 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] M. Amasaki: "On the basic sequences of integral curves in P^3"Proceedings of the 23rd symposium on commutative algebra, Kurashiki, November 19-22, 2001. 58-67 (2002)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2001 Final Research Report Summary
  • [Publications] Mutsumi Amasaki: "Homogeneous prime ideals and graded modules fitting into long Bourbaki sequences"Journal of Pure and Applied Algebra. 162. 1-21 (2001)

    • Related Report
      2001 Annual Research Report
  • [Publications] Mutsumi Amasaki: "On the basic sequences of integral curves in P^3"第23回可換環論シンポジウム報告集. 58-67 (2002)

    • Related Report
      2001 Annual Research Report
  • [Publications] Mutsumi Amasaki: "Generic Groebner bases and Weierstrass bases of homogeneous submodules of graded free modules"Journal of Pure and Applied Algebra. 152. 3-16 (2000)

    • Related Report
      2000 Annual Research Report
  • [Publications] Mutsumi Amasaki: "Homogeneous prime ideals and graded modules fitting into long Bourbaki sequences"Journal of Pure and Applied Algebra. (掲載決定).

    • Related Report
      2000 Annual Research Report

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Published: 2000-04-01   Modified: 2016-04-21  

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