2011 Fiscal Year Final Research Report
Studies on global problems on non commutative algebraic geometry
| Project/Area Number |
20540046
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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 | Kochi University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
JUN' ICHI Matsuzawa 奈良女子大学, 理学部, 教授 (00212217)
KENTARO Yoshitomi 大阪府立大学, 総合教育研究機構, 講師 (10305609)
KATSUHIKO Kikuchi 京都大学, 大学院・理学研究科, 助教 (50283586)
TAKURO Mochizuki 京都大学, 数理解析研究所, 准教授 (10315971)
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| Co-Investigator(Renkei-kenkyūsha) |
AKIRA Ishii 広島大学, 理学研究科, 准教授 (10252420)
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| Research Collaborator |
HAJIME Kuroiwa 高知大学, 総合人間自然科学研究科, 博士課程
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| Project Period (FY) |
2008 – 2011
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| Keywords | 非可換代数幾何学 / 射影幾何学 / 射影的加群 / Dixmier予想 / Jacobian問題 |
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| Research Abstract |
For any symplectic polynomial endomorphism of an affine space, the representative defined a sheaf on the affine space. Its triviality is equivalent to the existence of a lift of the map to an Endomorphism of a Weyl algebra. Next we have used the theory of Abe-Yoshinaga on a behavior of reflexive sheaves on the hyperplane at infinity and obtained a result which says that the absence of the singularity on the infinity implies an existence of a` quantization' of a symplectic endomorphism of an affine space. This gives an evidence of effectiveness of ordinary commutative algebraic geometry of' compact' spaces such as projective spaces in dealing with non commutative objects.
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