论文部分内容阅读
The group of automorphisms of the complex affine plane has a well known structure as an amalgamated free product of the triangular and affine subgroups.As such,every automorphism has a unique polydegree,the sequence of degrees of the triangular automorphisms in any factorization.The automorphism group also can be given the structure of an infinite dimensional algebraic variety.The interaction between these two structures is not yet well understood.We will discuss the general problem and a new result that a class of automorphisms with a polydegree of length one are contained in the closure (in the Zariski topology)of a set of automorphisms with a polydegree of length three.In particular,this provides a counterexample to a conjecture of Furter.This is joint work with Eric Edo.