most citedShestakov-Umirbaev reductions and Nagata's conjecture on a polynomial automorphism

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math.AC2008★ 2 cited

Shestakov-Umirbaev reductions and Nagata's conjecture on a polynomial automorphism

Shigeru Kuroda

In 2003, Shestakov-Umirbaev solved Nagata's conjecture on an automorphism of a polynomial ring. In the present paper, we reconstruct their theory by using the "generalized Shestako…

math.AC2007★ 1 cited

Automorphisms of a polynomial ring which admit reductions of type I

Shigeru Kuroda

Recently, Shestakov-Umirbaev solved Nagata's conjecture on an automorphism of a polynomial ring. To solve the conjecture, they defined notions called reductions of types I--IV for…

math.AC2007

A generalization of the Shestakov-Umirbaev inequality

Shigeru Kuroda

We give a generalization of the Shestakov-Umirbaev inequality which plays an important role in their solution of the tame generators conjecture.