| Project/Area Number |
17540088
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Kagoshima University |
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Principal Investigator |
YOKURA Shoji Kagoshima University, Dept. of Math. & Comp. Sci., Professor, 理学部, 教授 (60182680)
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| Co-Investigator(Kenkyū-buntansha) |
TSUBOI Shoji Kagoshima University, Dept. of Math. & Comp. Sci., Professor, 理学部, 教授 (80027375)
MIYAJIMA Kimio Kagoshima University, Dept. of Math. & Comp. Sci., Professor, 理学部, 教授 (40107850)
AIKOU Tadashi Kagoshima University, Dept. of Math. & Comp. Sci., Professor, 理学部, 教授 (00192831)
OHMOTO Toru Hokkaido University, Graduate School of Sci., Associate Professor, 大学院理学研究科, 助教授 (20264400)
AOYAMA Kiwamu Kagoshima University, Dept. of Math. & Comp. Sci., Lecturer, 理学部, 講師 (70202497)
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| Project Period (FY) |
2005 – 2006
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| Project Status |
Completed (Fiscal Year 2006)
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| Budget Amount *help |
¥3,300,000 (Direct Cost: ¥3,300,000)
Fiscal Year 2006: ¥1,400,000 (Direct Cost: ¥1,400,000)
Fiscal Year 2005: ¥1,900,000 (Direct Cost: ¥1,900,000)
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| Keywords | singular variety / characteristic class / motivic measure / relative Grothendieck group / bivariant theory / equivariant characteristic class / モチビック積分 / 同変特性ホモロジー類 |
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| Research Abstract |
(1) We constructed a general theory of characteristic classes of symbolic algebraic varieties, using Fulton-MacPherson's bivariant theory.
(2) In a joint work with J.-P. Brasselet and J. Schurmann I succeeded in the construction of Hirzebruch classes of singular varieties, which is a class version of the singular Hirzebruch genera.
(3) Using the theorems obtained in the above (2), we obtained stringy characteristic classed and arc characteristic classes, which are a generalization of the stringy Chern class and arc Euler chracteristic.
(4) The existence of a bivariant Chern class was conjectured by Fulton and MacPherson and in 1981J.-P. Brasselet solved it affirmatively under a certain condition. Since then, its uniqueness has been an open problem. In 2002 the head investigator, Yokura, has shown its uniqueness for any morphism with the smooth target. Extending this result furthermcre, the head investigator, together with Brasselet and Schurmann, obtained some theorems concerning its uniqueness.
(5) Generalizing the results obtained in the above (4), we proved some theorems concerning bivariant characteristic classes, which may be considered as a (poartial) positive answer to a uniqueness problem in Fulton-MacPherson's bivariant theory.
(6) A fundamental thing in the construction of characterisic classes of symbolic algebraic varieties is that bifunctors play a key role. Based on this observation, we proposed to capture Levine-Morel's algebraic cobordism as a bivariant theory or to extend it to a bivariant theory, and we obtained some results to support this proposal.
(7) The head investigator, together with Schurmann, published a survey article of characteristic classes of singular spaces (about 90 oages).
(8) Unfortuntely we could not carry out a program of capturing equivariant characteristic classes as a special case of a general theory of characteristic classes of symbolic algebraic varieties.
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