On group structure associated to Jacobian pairs with mixed leading forms Original Research Article

Abhyankar had shown that in order to solve the Jacobian Conjecture, it suffices to rule out the existence of Jacobian pairs with mixed leading form. Assume that such a pair {f, g} exists. Following Abhyankar, consider the Laurent series expansion of {f, g} at infinity. Part of the coefficients of the series becomes invariants of certain group action. We also obtain several old results proved by Moh by investigating the associated group action.