A new inversion formula for a polynomial map in two variables (Q1181417)

Let \(k\) be an arbitrary field, \(F:=(F_ 1,F_ 2):k^ 2\to k^ 2\) be an invertible polynomial map. Write \(F_ i(TV)\) for \(F_ i(TV_ 1,TV_ 2)\) and let the \(T\)- resultant be \(R:=R_ T(F_ 1(TV)-Y_ 1,F_ 2(TV)-Y_ 2)\). The authors prove that the inverse \(G:=(G_ 1,G_ 2)\) of \(F\) fulfills \(R=a(V)(V_ 1G_ 2-V_ 2G_ 1)\), yielding as a corollary the inversion formula \(G_ 1-V_ 1G_ 2=R(Y,V_ 1,1)/R(F(1,0),V_ 1,1)\).