2000 Fiscal Year Annual Research Report

特異多様体の特性類とモチーフおよびその周辺に関する研究

Research Project

Project/Area Number	12640081
Research Institution	Kagoshima University
Principal Investigator	與倉昭治鹿児島大学, 理学部, 教授 (60182680)
Co-Investigator(Kenkyū-buntansha)	大本亨鹿児島大学, 理学部, 助教授 (20264400) 宮嶋公夫鹿児島大学, 理学部, 教授 (40107850) 坪井昭二鹿児島大学, 理学部, 教授 (80027375) 青山究鹿児島大学, 理学部, 講師 (70202497) 小柴洋一鹿児島大学, 理学部, 助教授 (00041773)
Keywords	特異多様体 / 特性類 / 同変理論 / モチーフ / ミルナー類 / 同変チャーン類
Research Abstract	1)Fulton-MacPhersonの本で述べられているoperational bivariant theoryについてのある主張に対して単純な反例を見つけた。それに示唆されて幾つかのconstructible functionのbivariant theoryを構成し、さらにFulton-MacPhersonの主張を改良した。 2)一般に、local complete intersection morphismについてはChern classに関するVerdier型Riemann-Rochは成立しないが、Zariski topologyでのfiber bundleについては成立することを証明した。 3)Yが非特異多様体のとき、写像f:X→Yに対するbivariant Chern classはuniqueに決定されることを証明した。より具体的には、bivariant constructible function αに対してbivariant Chern class γ(α)はf^s(TY)∩c_(α)と表わせることを証明した。ここに、s(TY)はYの接束のSegreコホモロジー類である。この結果は「Sが非特異な曲線のとき、写像f:X→Sに対するBrasseletのbivariant Chern classとSabbahのbivariant Chern classは一致する」というZhouの定理(1995)の別証を与えたことになる。 4)同様にして、Fulton-MacPhersonの本で構成されたbivariant Riemann-Rochについても、Yが非特異多様体のとき、写像f:X→Yに対するbivariant Riemann-Rochはuniqueに決定されることを証明した。 5)f^s(TY)∩c_(α)の諸性質を調べ、合成積に関するGinzburg型の定理を証明した。

Research Products

(11 results)

All Other

All Publications (11 results)

[Publications] J.-P.Brasselet and Shoji Yokura: "Remarks on bivariant constructible functions,"Advanced Studies in Pure Mathematics. 29. 53-77 (2000)
[Publications] Toru Ohmoto and Shoji Yokura: "Product formulas for Milnor classes"Bulletin Polish Acad.Sci.. 48(4). 387-401 (2000)
[Publications] Shoji Yokura: "An application of bivariant theory to Milnor classes"Topology and Its Applications. (印刷中). 19 (2001)
[Publications] Lars Ernstrom and Shoji Yokura: "On bivariant Chern-Schwartz-MacPherson classes with values in bivariant Chow groups"Erwin Schrodinger Institute Preprint Series. 891. 21 (2000)
[Publications] Shoji Yokura: "Bivariant theories of constructible functions and Grothendieck transformations,"Erwin Schrodinger Institute Preprint Series. 930. 21 (2000)
[Publications] Shoji Yokura: "Verdier-Riemann-Roch for Chern class and Milnor class"Erwin Schrodinger Institute Preprint Series. 933. 24 (2000)
[Publications] Shoji Tsuboi: "Infinitesimal Parameter Spaces of Locally Trivial Deformations of Compact Complex Surfaces with Ordinary Sungularities"Finite or Infinite Dimensional Complex Analysis (Marcel Dekker.Inc.).. 523-532 (2000)
[Publications] Shoji Tsuboi and F.Guillen: "Simultaneous Cubic Hyper-resolutins of Locally Trivial Analytic Families of Complex Projective Varieties and Cohomological Descent"The Reprots of the Faculty of Science Kagoshima University. 33. 1-33 (2000)
[Publications] Shoji Tsuboi: "A Certain Degenerate Ordinary Singularity of Dimension Three"Proceedings of the Eighth International Conference on Finite or Infinite Dimensional Complex Analysis, Shandon University. (印刷中).
[Publications] Kimio Miyajima: "CR geometry/analysis and deformation of isolated singularities"J.Korean Math.Soc.. 37(2). 193-223 (2000)
[Publications] Yoichi Koshiba: "On the caluculations of the coefficients of the cyclotomic polynomials II"The Reports of the Faculty of Science Kagoshima University. 33. 55-59 (2000)

2000 Fiscal Year Annual Research Report

特異多様体の特性類とモチーフおよびその周辺に関する研究

Principal Investigator

與倉 昭治 鹿児島大学, 理学部, 教授 (60182680)

Research Products

[Publications] J.-P.Brasselet and Shoji Yokura: "Remarks on bivariant constructible functions,"Advanced Studies in Pure Mathematics. 29. 53-77 (2000)

[Publications] Toru Ohmoto and Shoji Yokura: "Product formulas for Milnor classes"Bulletin Polish Acad.Sci.. 48(4). 387-401 (2000)

[Publications] Shoji Yokura: "An application of bivariant theory to Milnor classes"Topology and Its Applications. (印刷中). 19 (2001)

[Publications] Lars Ernstrom and Shoji Yokura: "On bivariant Chern-Schwartz-MacPherson classes with values in bivariant Chow groups"Erwin Schrodinger Institute Preprint Series. 891. 21 (2000)

[Publications] Shoji Yokura: "Bivariant theories of constructible functions and Grothendieck transformations,"Erwin Schrodinger Institute Preprint Series. 930. 21 (2000)

[Publications] Shoji Yokura: "Verdier-Riemann-Roch for Chern class and Milnor class"Erwin Schrodinger Institute Preprint Series. 933. 24 (2000)

[Publications] Shoji Tsuboi: "Infinitesimal Parameter Spaces of Locally Trivial Deformations of Compact Complex Surfaces with Ordinary Sungularities"Finite or Infinite Dimensional Complex Analysis (Marcel Dekker.Inc.).. 523-532 (2000)

[Publications] Shoji Tsuboi and F.Guillen: "Simultaneous Cubic Hyper-resolutins of Locally Trivial Analytic Families of Complex Projective Varieties and Cohomological Descent"The Reprots of the Faculty of Science Kagoshima University. 33. 1-33 (2000)

[Publications] Shoji Tsuboi: "A Certain Degenerate Ordinary Singularity of Dimension Three"Proceedings of the Eighth International Conference on Finite or Infinite Dimensional Complex Analysis, Shandon University. (印刷中).

[Publications] Kimio Miyajima: "CR geometry/analysis and deformation of isolated singularities"J.Korean Math.Soc.. 37(2). 193-223 (2000)

[Publications] Yoichi Koshiba: "On the caluculations of the coefficients of the cyclotomic polynomials II"The Reports of the Faculty of Science Kagoshima University. 33. 55-59 (2000)

與倉昭治鹿児島大学, 理学部, 教授 (60182680)