Study of polynomial rings : establishment of effective methods and their applications

多项式环的自同构是多项式环论（仿射代数几何）的主要研究对象之一。2003年，Shestakov-Umirbaev发表了划时代的三元多项式环自同构理论，解决了长期悬而未决的Nagata猜想。继Shestakov-Umirbaev的研究之后，我们建立了一个分析三元多项式环自同构的有效方法，并证明了一些有趣的定理作为应用.

Automorphisms of a polynomial ring are one of the main objects of study in Polynomial Ring Theory(Affine Algebraic Geometry). In 2003, Shestakov-Umirbaev published an epoch-making theory on automorphisms of a polynomial ring in three variables, and solved Nagata's conjecture which was open for a long time. Following the study of Shestakov-Umirbaev, we establish a useful and powerful method for analyzing automorphisms of polynomial rings in three variables, and proved various interesting theorems as applications.