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On polynomial curves in the affine plane

A curve that can be parametrized by polynomials is called a polynomial curve. It is well-known that a polynomial curve has only one place at infinity. Sathaye indicated the Abhyankar’s question for curves with one place at infinity. Let C be a curve with one place at infinity. Is there a polynomial curve associated with the semigroup generated by pole orders of C at infinity? We found a counter example for the Abhyankar’s question using Grobner basis computation. In this paper, we give the details.