2 citations · 3 across the 3 of their papers we have counts for
3 papers
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.