Newton polygons of jacobian pairs (Q1175214)

A pair of polynomials \(f,g\in k[x,y]\) is said to be jacobian if \({\partial f\over \partial x}\cdot{\partial g\over \partial y}-{\partial f\over \partial y}\cdot {\partial g\over \partial x}\) is a nonzero element of the field \(k\). The main result of this paper shows that if \((f,g)\) is a jacobian pair, then the Newton polygons of \(f\) and \(g\) are similar. The author notes that the result has been established by Abhyankar in unpublished notes from the early 70's. The techniques of the proof presented here are from \textit{S. S. Abhyankar}'s (published) notes: ``Expansion techniques in algebraic geometry'', Tata Inst. Fund. Res., Lect. Math. 57 (Bombay 1977).