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2001 Fiscal Year Final Research Report Summary

Classification of higher dimensional hypersurface singularities in terms of non-degenerate complete intersections

Research Project

Project/Area Number 12640020
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  Kanazawa University, Faculty of sciences, Associate professor, 理学部, 助教授 (60183878)

Co-Investigator(Kenkyū-buntansha) KODAMA Akio  Kanazawa University, Faculty of sciences, Professor, 理学部, 教授 (20111320)
ISHIMOTO Hiroyasu  Kanazawa University, Faculty of sciences, Professor, 理学部, 教授 (90019472)
FUJIMOTO Hirotaka  Kanazawa University, Faculty of sciences, Professor, 理学部, 教授 (60023595)
MORISHITA Masanori  Kanazawa University, Faculty of sciences, Associate professor, 理学部, 助教授 (40242515)
HAYAKAWA Takayuki  Kanazawa University, Graduate school of natural science and technology, Assistant, 自然科学研究科, 助手 (20198823)
Project Period (FY) 2000 – 2001
Keywordsblowing up / multiplicity / isoloted singularity / rational singulerity / value distrilution theony / terminal singulauty / Milnor number / divisor class group
Research Abstract

On the main theme of this project :
(1) In 2000, M. Tomari studied the nitration of ideals on terminal singularities where the associated graded rings are integral domains with isolated singularity. As a special case, he showed the regularity of their associated graded rings of 3-dimensional regular local ring. In 1 2001, Tomari gave an inequality about Milnor number μ(f) of a hypersurface isolated singularity Uin terms of weighted Taylor expansion of the defining equation f. Here the equality holds iiand only if the initial form defines an isolated singularity. This gives a characterization of a semiquasi-homogeneous condition in terms of μ. The proof uses a result of Tomari on multiplicity of filtered ring.
(2) T. Hayakawa studied several partial resolutions of 3-dimensipnal terminal singularities with index is not less than two. In 2000, he constructed an interesting example which admits a partial resolution where at worst Gorenstein terminal singularities remain. This was understood naturally by the' studies of the special partial resolution of rational double points which appears as the general members of anti-canonical linear system of the singularity. In 2001 he also studied the irreducible components of this type of partial resolution.
As related-works on complex analysis :
(3) H. Fujimoto had succeeded to construct a new series of examples of hyperbolic hypersurfaces of degree 2^n in n-dimensional complex protective spaces. In the case of n = 2, this example gives the world record of the minimal possible degree of the ambient spaces for such situation.
(4) A. Kodama studied the general ellipsoids with not necessary smooth boundaries from the points of view of the Webster metric.

  • Research Products

    (16 results)

All Other

All Publications (16 results)

  • [Publications] S.Ishii., M.Tomari: "Hyper surface non-rational singularities which look canonical from their Newton boundaries"Math. Zeitschrift. 237. 125-147 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Tomari., K.-i.Watanabe: "Cyclic covers of normal graded rings"Kodai Math. J.. 24. 436-357 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Tomari: "Multiplicity of filtered rings and simple K3 singularities of multiplicity two"Publ. RIMS, Kyoto Univ.. (to appear).

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] T.Hayakawa: "Blowing ups of 3-dimensional terminal singularities II"Publ. RIMS, Kyoto Univ. 36. 423-456 (2000)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] H.Fujimoto: "A family of hyperbolic hypersurfaces in the complex space"Complex Variables. 43. 273-283 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] M.Morishita: "A theory of genera for cyclic coverings of links"Proc. Japan Academy. 77. 115-118 (2001)

    • Description
      「研究成果報告書概要(和文)」より
  • [Publications] S. Ishii, M. Tomari: "Hypersurface non-rational singularities which look canonical from their Newton boundaries"Math. Zeitshrift. 237. 125-147 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M. Tomari, K. -I. Watanabe: "Cyclic covers of normal graded rings"Kodai Math. J.. 24. 436-457 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M. Tomari: "Multiplicity of filtered rings and simple K3 singularities of multiplicity two"Publ. Res. Inst. Math. Sci. Kyoto Univ.. (to appear).

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] T. Hayakawa: "Blowing ups of 3-dimensional terminal singularities"II. Publ. Res. Inst. Math. Sci. Kyoto Univ.. 36. 423-456 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H. Fujimoto: "On uniqueness of meromorphic functions sharing finite sets"Amer. J. Math.. 122. 1175-1203 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] H. Fujimoto: "A family of hyperbolic hypersurfaces in the complex space"Complex Variables. 43. 273-283 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] A. Kodama: "A remark on generalized complex ellipsoids with spherical boundary points"J. korean Math. Soc.. 37. 285-295 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M. Morishita: "Milnor's link invariants attached to certain Galois groups over Q"Proc. Japan Academy. 76. 18-21 (2000)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M. Morishita, and T. Watanabe: "Adele Geometry of Numbers, Class Field Theory - its Centenary and Prospect (ed. By K. Miyake)"The Adv. Stud, in Pure. Math.. 30. 509-536 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
  • [Publications] M. Morishita: "A theory of genera for cyclic coverings of links"Proc. Japan Academy. 77. 115-118 (2001)

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

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Published: 2003-09-17  

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