2005 Fiscal Year Final Research Report Summary
Algebraic group actions and the structure of affine algebraic varieties
| Project/Area Number |
15540043
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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 |
Algebra
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| Research Institution | University of Hyogo (2004-2005)
Himeji Institute of Technology (2003) |
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Principal Investigator |
MASUDA Kayo University of Hyogo, Graduate school of Material Science, Associated Professor, 大学院・物質理学研究科, 助教授 (40280416)
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| Co-Investigator(Kenkyū-buntansha) |
MIYANISHI Masayoshi Kwansei Gakuin University, School of Science and Technology, Professor, 理工学部, 教授 (80025311)
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| Project Period (FY) |
2003 – 2005
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| Keywords | affine pseudo-plane / Cancellation Problem / Makar-Limanov invariant / Linearization Problem / Jacobian Conjecture / A^1-fibration / algebraic torus action |
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| Research Abstract |
1.Linearization Problem
We have had some results on the Cancellation Problem which is closely related to the Linearization Problem.
(1)There exists an infinite dimensional family of affine pseudo-planes without cancellation property. Furthermore, tom Dieck surfaces are characterized as affine pseudo-planes with nontrivial actions of an algebraic torus.
(2)The kernel of a triangular derivation with a slice is a polynomial ring.
2.Generalized Jacobian Problem
(1)We studied the Jacobian Problem for smooth affine surfaces with A^1-fibrations, especially, affine pseudo-planes. We succeeded in making clear of the structure of affine pseudo-planes to some extent with joint work with R.V.Gurjar and P.Russell, but could not resolve the Generalized Jacobian Problem for affine pseudo-planes.
(2)Miyanishi showed that the Generalized Jacobian Problem for affine pseudo-planes has an affirmative answer if they satisfy the generalized Sard property.
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