2011 Fiscal Year Final Research Report
Study of polynomial rings : establishment of effective methods and their applications
| Project/Area Number |
21740026
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | Tokyo Metropolitan University |
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Principal Investigator |
KURODA Shigeru 首都大学東京, 大学院・理工学研究科, 准教授 (70453032)
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| Project Period (FY) |
2009 – 2011
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| Keywords | 可換環論 / 多項式環論 / アフィン代数幾何学 / 多項式自己同型 |
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| Research Abstract |
Automorphisms of a polynomial ring are one of the main objects of study in Polynomial Ring Theory(Affine Algebraic Geometry). In 2003, Shestakov-Umirbaev published an epoch-making theory on automorphisms of a polynomial ring in three variables, and solved Nagata's conjecture which was open for a long time. Following the study of Shestakov-Umirbaev, we establish a useful and powerful method for analyzing automorphisms of polynomial rings in three variables, and proved various interesting theorems as applications.
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