Abstract
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. Let $C$ be a curve with one place at infinity. Sathaye presented the following question raised by Abhyankar: Is there a polynomial curve associated with the semigroup generated by pole orders of $C$ at infinity? In this paper, we give a negative answer to this question using Gröbner basis computation.
Citation
Mitsushi Fujimoto. Masakazu Suzuki. Kazuhiro Yokoyama. "On polynomial curves in the affine plane." Osaka J. Math. 43 (3) 597 - 608, September 2006.
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