This article may be written in a style that is too abstract to be readily understandable by general audiences. (April 2022) |
Field | Algebraic geometry |
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Conjectured by | Masayoshi Nagata |
Conjectured in | 1972 |
First proof by | Ualbai Umirbaev and Ivan Shestakov |
First proof in | 2004 |
In algebra, Nagata's conjecture states that Nagata's automorphism of the polynomial ring k[x,y,z] is wild. The conjecture was proposed by Nagata (1972) and proved by Ualbai U. Umirbaev and Ivan P. Shestakov (2004).
Nagata's automorphism is given by
where .
For the inverse, let Then and . With this and .