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Research on Complex Analytic Geometry and Singularity Theory

Research Project

Project/Area Number 07454011
Research Category

Grant-in-Aid for Scientific Research (B)

Allocation TypeSingle-year Grants
Section一般
Research Field Geometry
Research InstitutionHokkaido University

Principal Investigator

SUWA Tatsuo  Hokkaido Univ., Grad.School of Sci., Prof., 大学院・理学研究科, 教授 (40109418)

Co-Investigator(Kenkyū-buntansha) OKA Mutsuo  Tokyo Metropolitan Univ., Fac.of Sci., Prof., 理学部, 教授 (40011697)
HONDA Naofumi  Hokkaido Univ., Grad.School of Sci., Lecturer, 大学院・理学研究科, 講師 (00238817)
KAWAZUMI Nariya  Hokkaido Univ., Grad.School of Sci., Assoc.Prof., 大学院・理学研究科, 助教授 (30214646)
NAKAI Isao  Hokkaido Univ., Grad.School of Sci., Assoc.Prof., 大学院・理学研究科, 助教授 (90207704)
ISHIKAWA Goo  Hokkaido Univ., Grad.School of Sci., Assoc.Prof., 大学院・理学研究科, 助教授 (50176161)
泉屋 周一  北海道大学, 大学院・理学研究科, 教授 (80127422)
山口 佳三  北海道大学, 大学院・理学研究科, 教授 (00113639)
中村 郁  北海道大学, 大学院・理学研究科, 教授 (50022687)
Project Period (FY) 1995 – 1996
Project Status Completed (Fiscal Year 1996)
Budget Amount *help
¥7,800,000 (Direct Cost: ¥7,800,000)
Fiscal Year 1996: ¥3,700,000 (Direct Cost: ¥3,700,000)
Fiscal Year 1995: ¥4,100,000 (Direct Cost: ¥4,100,000)
Keywordsvector fields / singular foliations / indices and residues / localization / characteristic classes / singular varieties / ベットル場 / 正則ベクトル場 / 留数
Research Abstract

The research was done mainly on the indices and residues of vector fields and holomorphic singular foliations, the charactreistic classes of singular varieties, the Cech-de Rham cohomology theory and integration theory on stratified spaces. Let us be more specific.
(1) Collaboration with J.Seade on the residue theorem for the Baum-Bott residues of foliations on open manifolds and its applications. The joint paper on this has been published in Mathematische Annalen.
(2) In another collaboration with J.Seade, we investigated various indices of vector fields on varieties with isolated singularities and we obtained an "adjunction formula" for such varieties. The results are written in a joint paper.
(3) As an application of the formula in (2), a formula for the Chem-Schwartz-MacPherson class of a local complete intersection variety with isolated singularities is obtained. The result has been published in C.R.Acad.Sci., Paris.
(4) As a generalization of the formula in (2), in a collaboration with D.Lehmann and J.Seade, we introduced a generalized Milnor number and obtained a similar formula for varieties with possibly non-isolated singularities. The results are written in a joint paper.
(5) In a joint work with B.Khanedani, we studied the invariants of singular holomorphic foliations on complex surfaces and obtained various formulas. The joint paper on these will appear in Hokkaido Math.J.
(6) In a joint work with T.Honda, we proved a residue formula for meromorphic functions on complex surfaces and gave some applications. The results are written in a joint paper.
(7) In a collaboration with J.-P.Brasselet, we studied the Nash modification associated with a sinular holomorphic foliation and, as an application, we proved a conjecture of Baum-Bott in some cases. The results are written in a joint paper.

Report

(3 results)
  • 1996 Annual Research Report   Final Research Report Summary
  • 1995 Annual Research Report
  • Research Products

    (24 results)

All Other

All Publications (24 results)

  • [Publications] D.Lehmann: "Residues of holoworphic vector fields vlafive to in variant subvuaricties" J. of Differential Geometry. 42. 165-192 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] I.Nakai: "Note on versal deformation of first order PDE_s and wel sti." J. of Differential Equations. 118. 253-292 (1995)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] T.Suwa: "Classes de Chern des intersections completes locales" C. R. Acid. Sei.,Paris. 324. 67-70 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] G.Ishikawa: "Symplectic and Lagrangian stabilities of qeu Whitney umbrellas" Invent. wath.126-2. 215-234 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] N.Kawazumi: "The primary appvoxiuation to the cohomology of the woluli space of curves and cocycler for the stabli cohomology classes" Math,Research Lett.3. 629-641 (1996)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] N.A'Campo: "Geowetoy of Nane curves via Tschirnhauser tower" Osaka J. Math.33. 1003-1004 (1997)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] D.Lehmann: "Residues of holomorphic vector fields relative to singular invariant subvarieties" J.of Differential Geom. 42. 165-192 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] I.Nakai: "Notes on versal deformation of first order PDEs and web structure" J.of Differential Equations. 118. 253-292 (1995)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] T.Suwa: "Classes de Chem des intersections completes locales" C.R.Acad.Sci.Paris. 324. 67-70 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] G.Ishikawa: "Symplectic and Lagrange stabilities of open Whitney umbrellas" Invent.math. Vol.126-2. 215-234 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] N.Kawazumi: "The primary approximation to the cohomology of the moduli space of curves and cocycles for the stable cohomology classes" Math.Research Lett.3. 629-641 (1996)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] N.A'Campo: "Geometry of plane curves via Tschirnhausen resolution tower" Osaka J.Math. 33. 1003-1034 (1997)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      1996 Final Research Report Summary
  • [Publications] D. Lehuman: "Resides of holoworphic vector fields vlative to invariant Subuarictres" J. of Differential Geometry. 42. 165-192 (1995)

    • Related Report
      1996 Annual Research Report
  • [Publications] I. Nakai: "Neter on vevsal deforvation of first order PDEs. and weli str :" J. of Differential Equatious. 118. 253-292 (1995)

    • Related Report
      1996 Annual Research Report
  • [Publications] T. Suwa: "Classes de Chern des intersections conpletes locales" C. R. Acaid. Sci. , Paris. 324. 67-70 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] G. Ishikawa: "Symplectic and Lazragian stsbilities of geu Whithey umbrellas" Invent. wath.126-2. 215-234 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] N. Kawazumi: "The primany appvoxiuation to the cohomology of the wobuli space of curves and coeycley for the stable cohomology classes" Math : Resewch Lett.3. 629-641 (1996)

    • Related Report
      1996 Annual Research Report
  • [Publications] N. A' Campo: "Geometry of Nane curves via Tschirnhausen tower" Osaka J. Math.33. 1003-1004 (1997)

    • Related Report
      1996 Annual Research Report
  • [Publications] T.Suwa: "Indices of holomovphic vector fields relatioe to inuariant curves on surfaces" Proc.of the Auer Math,Soc.123. 2989-2997 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] D.Lehmann,K and T.Suwa: "Residues of holomorphic vector fields velative to singular invariant subvarietics" J.of Rift.Geom.41. 165-192 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] I.Nakamura: "Moishezon threcfolds boueomoplric to a cibic bysecsubace in P^4" J.Algeluaic Geovnetry. 印刷中 (1996)

    • Related Report
      1995 Annual Research Report
  • [Publications] S.Izumiya: "Coupletely iutegrable holoromic uystems of fist order difberential eguations" Pooc.of the Royal Society of Edinkungh.125A. 567-586 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] S.Izumiya and W.Marar: "On topologically stalele siugular seufacer in a 3-warifold" J.of Geonetry. 52. 108-119 (1995)

    • Related Report
      1995 Annual Research Report
  • [Publications] G.Ishikawa: "Develspable of a ucrve and determinacy elatuie to osaulation type" Quart.J.Meth.Oxford. 46. 437-451 (1995)

    • Related Report
      1995 Annual Research Report

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Published: 1995-04-01   Modified: 2016-04-21  

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