Nagata's conjecture

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).

For the conjecture about curves, see Nagata's conjecture on curves.
Nagata's conjecture
FieldAlgebraic geometry
Conjectured byMasayoshi Nagata
Conjectured in1972
First proof byUalbai Umirbaev and Ivan Shestakov
First proof in2004

Nagata's automorphism is given by

References
  • Nagata, Masayoshi (1972), On automorphism group of k[x,y], Tokyo: Kinokuniya Book-Store Co. Ltd., MR 0337962
  • Umirbaev, Ualbai U.; Shestakov, Ivan P. (2004), "The tame and the wild automorphisms of polynomial rings in three variables", Journal of the American Mathematical Society, 17 (1): 197–227, doi:10.1090/S0894-0347-03-00440-5, ISSN 0894-0347, MR 2015334
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.