Nagata's conjecture - Alchetron, The Free Social Encyclopedia

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

( x , y , z ) ↦ ( x − 2 ( x z + y 2 ) y − ( x z + y 2 ) 2 z , y + ( x z + y 2 ) z , z ) .

References

Nagata's conjecture Wikipedia

(Text) CC BY-SA