Project/Area Number  02452001 
Research Category 
GrantinAid for General Scientific Research (B)

Allocation Type  Singleyear Grants 
Research Field 
代数学・幾何学

Research Institution  Hokkaido University 
Principal Investigator 
SUWA Tatsuo Hokkaido University, Faculty of Science Professor, 理学部, 教授 (40109418)

CoInvestigator(Kenkyūbuntansha) 
NAKAI Isao Hokkaido University, Faculty of Science Lecturer, 理学部, 講師 (90207704)
TOSE Nobuyuki Hokkaido University, Faculty of Science Associate Professor, 理学部, 助教授 (00183492)
ISHIKAWA GOO Hokkaido University, Faculty of Science Associate Professor, 理学部, 助教授 (50176161)
IZUMIYA Shyuichi Hokkaido University, Faculty of Science Associate Professor, 理学部, 助教授 (80127422)
SUZUKI Haruo Hokkaido University, Faculty of Science Professor, 理学部, 教授 (80000735)
中村 郁 北海道大学, 理学部, 助教授 (50022687)
田中 昇 北海道大学, 理学部, 教授 (80025296)

Project Period (FY) 
1990 – 1991

Project Status 
Completed(Fiscal Year 1991)

Budget Amount *help 
¥6,700,000 (Direct Cost : ¥6,700,000)
Fiscal Year 1991 : ¥2,300,000 (Direct Cost : ¥2,300,000)
Fiscal Year 1990 : ¥4,400,000 (Direct Cost : ¥4,400,000)

Keywords  Complex analytic geometry / Singularity theory / Singular foliation / Unfolding theory / Singular set / 特異点の留数 / 時異葉層構造 / 開析理論 / 解複体 / 特性多様体 
Research Abstract 
The head investigators and the investigators did research in Complex Analytic Geometry and Singularity Theory. Especially, on the research of the singularities of complex analytic foliations which was proposed in the research plans for this project, a survey article was written summarizing the results on the unfolding theory, the determinacy problem, the structure of the singular set and the invariants associated to it which have been obtained mainly by the head investigator. This was presented at the College on Singularity Theory held in Trieste, Italy during the summer of 1991. Also, as to the invariants associated to the singular set, the BaumBott residues and the newly found Lehmann residues are studied and the fundamental principle underlying the appearance of these invariants is clarified and some generalizations of them are considered. As to the application of the Dmodule theory, which was proposed in the previous year, the investigations of the characteristic variety and the
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local structure of thesolution complex of the Dmodule associated to a complex analytic singular foliation and their relation with the aforementioned invariants are continued. Besides the collaboration of the above research, each of the investigators did research on his own subject as well and obtained many results on thefollowing subject : Holonomy groupoids for generalized foliations and the ChernSimonsMaslov classes for symplectic boundles (Suzuki), applications of the singularity theory to the theory of differential equations, especially study of systems of completely integrable first order differential equations (Izumiya), singularity which appear in the projective geometry of curves and the maslov classes of Lagrangian varieties (Ishikawa), the microlocal analysis and its applications, especially the Morse inequality for Rconstructible sheaves (Tose), analytic group actions on the complex plane, especially the existence of the separatrix and the proof of the rigidity theorem (Nakai). Less
