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1996 Fiscal Year Final Research Report Summary

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)
Project Period (FY) 1995 – 1996
Keywordsvector fields / singular foliations / indices and residues / localization / characteristic classes / singular varieties
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.

  • Research Products

    (12 results)

All Other

All Publications (12 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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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
  • [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

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Published: 1999-03-09  

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