Some reductions on Jacobian problem in two variables

Let f=(f1,f2) be a regular sequence of affine curves in . Under some reduction conditions achieved by composing with some polynomial automorphismsof , we show that the intersection number of curves (fi) in equals to the coefficient of the leading term xn−1 in g2, where n=degfi (i=1,2) and (g1,g2) is the unique solution of the equation with deggi n−1. So the well-known Jacobian problem is reduced to solving the equation above. Furthermore, by using the result above, we show that the Jacobian problem can also be reduced to a special family of polynomial maps.