The $D$-resultant, singularities and the degree of unfaithfulness
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- by Arno van den Essen and Jie-Tai Yu PDF
- Proc. Amer. Math. Soc. 125 (1997), 689-695 Request permission
Abstract:
We introduce the $D$-resultant of two polynomials in one variable and show how it can be used to decide if $k(f(t),g(t))=k(t),k[f(t),g(t)]=k[t]$ and to find the singularities of the curve $x=f(t),y=g(t)$. The second criterion is used to give a very short proof of a special case of the epimorphism theorem of Abhyankar and Moh.References
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Additional Information
- Arno van den Essen
- Affiliation: Department of Mathematics, University of Nijmegen, Toernooiveld, 6525 ED Nijmegen, The Netherlands
- Email: essen@sci.kun.nl
- Jie-Tai Yu
- Affiliation: Department of Mathematics, University of Hong Kong, Hong Kong
- Email: yujt@hkusua.hku.hk
- Received by editor(s): June 15, 1995
- Received by editor(s) in revised form: September 21, 1995
- Communicated by: Wolmer V. Vasconcelos
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 689-695
- MSC (1991): Primary 13P99
- DOI: https://doi.org/10.1090/S0002-9939-97-03639-3
- MathSciNet review: 1353403