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Algebro-geometric studies of rational singularities and related singularities by blowing-ups

Research Project

Project/Area Number 09640021
Research Category

Grant-in-Aid for Scientific Research (C)

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

Principal Investigator

TOMARI Masataka  Graduate school of natural science and technology, Kanazawa University Associate professor, 自然科学研究科, 助教授 (60183878)

Co-Investigator(Kenkyū-buntansha) MORISHITA Masanori  Fuculty of sciences, Associate professor, 理学部, 助教授 (40242515)
HAYAKAWA Takayuki  Fuculty of sciences, Assistant, 理学部, 助手 (20198823)
KODAMA Akio  Fuculty of sciences, Professor, 理学部, 教授 (20111320)
ISHIMOTO Hiroyasu  Fuculty of sciences, Professor, 理学部, 教授 (90019472)
FUJIMOTO Hitotaka  Fuculty of sciences, Professor, 理学部, 教授 (60023595)
Project Period (FY) 1997 – 1998
Project Status Completed (Fiscal Year 1998)
Budget Amount *help
¥2,900,000 (Direct Cost: ¥2,900,000)
Fiscal Year 1998: ¥1,000,000 (Direct Cost: ¥1,000,000)
Fiscal Year 1997: ¥1,900,000 (Direct Cost: ¥1,900,000)
Keywordsthe normal graded rings / rational singularities / weighted blowing-ups / conjecture of M.Reid / the Segre product / terminal singularities / the arithemetic genus / the special log forms / ネバンリンナ理論 / 単純K3特異点 / 因子的ブロ-イングアップ / 正則曲線の一意性定理 / 多様体のホモトピー同値 / 正則自己同型群 / アデ-ル幾何学
Research Abstract

On the main theme of this project :
(1)In 1997, M.Tomari found more 3 examples of simple K3 singularities which do not belong to the famous 95 classess. It was a natural continuation of studies of previous year. Tomari also found a. counter example to an analogus conjecture of M.Reid about 4-dimensional terminal singularities in terms of Newton boundary. In the both studies, the theory of filtered blowing-up by Tomari-Watanabe plays an essential role. In 1998, Tomari succeeded to prove the criterion about the rational singularities and isolated singularities about the Segre product of two normal graded rings. The criterions are natural generalizations to those for the normal graded rings in terms of Pinkham-Demazure's construction.
(2)T.Hayakawa studied several partial resolutions of 3-dimensional terminal singularities by weighted blowing-ups. In particular he succeded to show a special corespondence between the set of divisorial blowing-ups with minimal discrepancy and the set of the maximal blowing-ups with "big weight". He classified the elementary contraction with the minimal discrepancy in his situation.
(3)M.Takamura gave a very good estiamte about the arithemetic genus of normal two-dimensional singularities of multiplicity two in terms of the Horikawa canonical resolution. Combined with the previous result of Tomari, he obtained the complete classification of the case of p_<alpha> = 2.
As related works on complex analysis :
(4)K.Morita studied the special log forms which gives a-basis of higher dimensional de Rham cohomology which is related to the arrangements of hyperfurface on the complex affine space. The work is aimed to give application to integral representaion of hypergeomeric functions of several variables and a natural generalization of Aomoto-Kita's theory.

Report

(3 results)
  • 1998 Annual Research Report   Final Research Report Summary
  • 1997 Annual Research Report
  • Research Products

    (20 results)

All Other

All Publications (20 results)

  • [Publications] T.Hayakawa: "Blowing ups of 3-dimensional terminal singularities" Publ.Res.Inst.Math.Sci.Kyoto Univ.to appear.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] K.Morita: "On the basis of twisted de Rham cohawology" Hokkaido Math. J.vol.27. 567-603 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Fujimoto: "Uniqueness problem with truncated multiplicities in value distribution theory II," Nagoya Math. J.to appear.

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] A.Kodama: "A characterization of certain weakly pseudoconvex domain" Tohoku Math. J.vol.51to appear. (1999)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] N.Kobayakawa and H.Ishimoto: "Homotopy classification of sufficiently connected manifolds" Sci.Rep.Kanazawa Univ.vol.43. 1-30 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Morishita and T.Watanabe: "On S-Hardy-Littlewood homogeneous spaces" Intern.J.Math.vol.9. 723-757 (1998)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] T.Hayakawa: "Blowing ups of 3-dimensinal terminal singularities" Publ.Res.Inst.Math.Sci.Kyoto Univ.(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] K.Morita: "On the basis of twisted de Rham cohomology" Hokkaido Math.J.vol.27. 567-603 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] H.Fujimoto: "Uniqueness problem with truncated multiplicities in value distribution theory II" Nagoya Math.J.(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] A.Kodama: "A characterization of certain weakly pseudoconvex domain" Tohoku Math.J.(to appear).

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] N.Kobayakawa and H.Ishimoto: "Homotopy classification of sufficiently connected manifolds" Sci.Rep.Kanazawa Univ.vol.43. 1-30 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] M.Morishita and T.Watanabe: "On S-Hardy-Littlewood homogeneous spaces" Intern J.Math.vol.9. 723-757 (1998)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1998 Final Research Report Summary
  • [Publications] T.Hayakawa: "Blowing ups of 3-dimensional terminal singularities" Pnbl.Res.Inst.Math.Sci.Kyoto Univ. to appear.

    • Related Report
      1998 Annual Research Report
  • [Publications] K.Morita: "On the basis of twisted de Rham cohomology" Hokkaido Math.J.vol 27. 567-603 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] H.Fujimoto: "Uniqueness problem with truncated multiplicities in value distribution theory II." Nagoya Math.J.to appear.

    • Related Report
      1998 Annual Research Report
  • [Publications] A.Kodama: "A characterization of certain weakly pseudoconvex domain" Tohoku Math.J.vol 51to appear. 未定 (1999)

    • Related Report
      1998 Annual Research Report
  • [Publications] N.Kobayakawa and H.Ishimoto: "Homotopy classification of sufficiently connected manifolds" Sci.Rep.Kanazawa Univ.vol 43. 1-30 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] M.Morishita and T.Watanabe: "On 5-Hardy Littlewood homogeneous spaces." Intern.J Math. vol 9. 723-757 (1998)

    • Related Report
      1998 Annual Research Report
  • [Publications] 藤本 坦孝: "Uniqueness problem with truncated multiplicities in value distribution theory" Nagoga Math.J.(to appear).

    • Related Report
      1997 Annual Research Report
  • [Publications] 森下 昌紀: "On a family of subgroups of the Teichmiillen modular group of genus two obtained from the Jones representation" J.of Math.Sci,Univ.of Tokyo. 4. 403-415 (1997)

    • Related Report
      1997 Annual Research Report

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Published: 1997-04-01   Modified: 2016-04-21  

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