Some Reductions on Jacobian Problem in Two Variables
نویسنده
چکیده
Let f = (f1, f2) be a regular sequence of affine curves in C. Under some reduction conditions achieved by composing with some polynomial automorphisms of C, we show that the intersection number of curves (fi) in C 2 equals to the coefficient of the leading term x in g2, where n = deg fi (i = 1, 2) and (g1, g2) is the unique solution of the equation yJ(f) = g1f1 + g2f2 with deg gi ≤ 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.
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