On Puiseux roots of Jacobians (Q1848132)

Let \(f(x,y)\) and \(g(x,y)\) be holomorphic germs, \(f,g: (\mathbb{C}^2,0) \to(\mathbb{C},0)\). The authors study properties of the zero arc \(x=\gamma(y)\) of the Jacobian determinant \(J(x,y)\) of \(f,g\) that it is not root of \(f\cdot g\). The authors obtain the factorization of \(J(x,y)\) in \(\mathbb{C} \{x,y\}\).