On polynomial curves in the affine plane
Fujimoto, Mitsushi ; Suzuki, Masakazu ; Yokoyama, Kazuhiro
Osaka J. Math., Tome 43 (2006) no. 2, p. 597-608 / Harvested from Project Euclid
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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.
Publié le : 2006-09-14
Classification:  14H50,  13P10,  68W30 
@article{1159190003,
     author = {Fujimoto, Mitsushi and Suzuki, Masakazu and Yokoyama, Kazuhiro},
     title = {On polynomial curves in the affine plane},
     journal = {Osaka J. Math.},
     volume = {43},
     number = {2},
     year = {2006},
     pages = { 597-608},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1159190003}
}

Fujimoto, Mitsushi; Suzuki, Masakazu; Yokoyama, Kazuhiro. On polynomial curves in the affine plane. Osaka J. Math., Tome 43 (2006) no. 2, pp.  597-608. http://gdmltest.u-ga.fr/item/1159190003/