Abstract
In this paper, by using the concept of resolvents of a prime ideal introduced by Ritt, we give methods for constructing a hypersurface which is birational to a given irreducible variety and birational transformations between the hypersurface and the variety. In the case of algebraic curves, this implies that for an irreducible algebraic curveC, we can construct a plane curve which is birational toC. We also present a method to find rational parametric equations for a plane curve if it exists. Hence we have a complete method of parameterization for rational algebraic curves.
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The work reported here was supported in part by the NSF Grants CCR-8702108 and 9117870
On leave from Institute of Systems Science, Academia Sinica, Beijing 100080, P.R. China
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Gao, XS., Chou, SC. On the parameterization of algebraic curves. AAECC 3, 27–38 (1992). https://doi.org/10.1007/BF01189021
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DOI: https://doi.org/10.1007/BF01189021