On weighted bidegree of polynomial automorphisms of C2
Abstract
Let F=(F1,F2):C2 ---> C2 be a polynomial automorphism. It is well know that deg F1 | deg F2 or deg F2 | deg F1. On the other hand, if (d1,d2) ∈ (N\0)2 is such that d1 | d2 or d2 | d1, then one can construct a polynomial automorphism F=(F1,F2) of C2 with deg F1=d1 and deg F2=d2. Let us fix w=(w1,w2) ∈ (N\0)2 and consider the weighted degree on C[x,y] with wdeg x=w1 and wdeg y=w2. In this note we address the structure of the set ( F1, F2) : (F1,F2) is an automorphism of C2.
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.