On group structure associated to Jacobian pairs with mixed leading forms (Q1358934)

Consider \(f,g \in {\mathbb{C}}[x,y]\) whose Jacobian is a non-zero constant. The Jacobian conjecture then says that \((f,g)\) has an algebraic inverse. After Abyankhar, Moh, Nagata et al., the Jacobian conjecture has been reduced to rule out the existence of \(f,g\), whose leading terms are of a particular form (so-called Jacobian pairs of mixed type). Taking such \(f,g\), the so-called \(A\)-expansion of \(f,g\) is considered and its coefficients are investigated. A group action on Jacobian pairs of mixed type is defined by changing of variables. The authors show that part of the coefficients of the series are invariants under this group action. Several old results of Moh are reproved.