The structure of affine algebraic varieties and the Linearization Problem

从代数群的作用，特别是加性群的作用的角度研究了仿射代数簇的结构。给出了包括仿射伪平面在内的一类仿射曲面的结构描述。通过加性群的作用，证明了线性化问题、消去问题和嵌入问题这三大开放问题之间存在着密切的关系。进一步，我们给出了在某些情况下高维仿射空间的代数作用的表征。

We studied the structure of affine algebraic varieties from the viewpoint of the actions of algebraic groups, especially the additive group. We gave a description of the structure of the affine surfaces of some type including the affine pseudo-plane. We show that there exists a close relationship among the big three open problems -- the Linearization Problem, Cancellation Problem, and the Embedding Problem-- through the action of the additive group. Further, we gave a characterization of the affine space of higher dimension in some cases by the algebraic actions.