Investigations in affine algebraic geometry

点击翻译按钮获取中文摘要

In "algebraic" geometry we study objects defined by polynomial (as opposed to simpler, e.g., linear, or more complicated, e.g. differentiable) equations. In this context "affine spaces", the linear spaces in the every day life of a mathematician, are familiar mainly as friendly shelters for objects that really interest us, a sphere in 3-space, for instance.Yet, when studied for their own sake, they soon begin to pose surprisingly thorny and largely unresolved questions: Which properties characterize them? What are their symmetries? What are the ways to embed one of them in another? These are some of the basic questions of "affine algebraic geometry". Some of the interrelated problems to be studied in this proposal are: To what extent are group actions on affine spaces linear? The study of surfaces very close to the affine plane in the sense that they have a very simple topology, e.g., are contractible. The study of plane rational curves and their embeddings in the affine plane. This research is a continuation of previous work and forms part of a large, lively international activity in this area.