Shestakov-Umirbaev inequality and automorphisms of a polynomial ring |
| S. Kuroda |
| Abstract |
| Recently, Shestakov-Umirbaev solved the tame generators conjecture. They gave a criterion to decide whether an automorphism of a polynomial ring in three variables is tame, and finally established that Nagata's automorphism is not tame. In their theory, a certain inequality on the degrees of polynomials plays a crucial role. In this talk, we generalize the Shestakov-Umirbaev inequality by a different technique, and give some applications of the generalized Shestakov-Umirbaev inequality. |