PARAMETERIZATION OF ALGEBRAIC SPACE-CURVES

This paper describes algorithms using Groebner basis techniques for pa rameterizing algebraic space curves. It is shown that the Groebner bas is of the ideal of a non-singular rational space curve of degree n in general position, taken with respect to an appropriate elimination ord er, has n + 1 elements whose degrees and structure can be precisely de scribed. The space curve can be parameterized by taking a birational p rojection to the plane and parameterizing the resulting plane curve. T he Groebner basis just described contains all the information necessar y to deal with the singularities introduced by projection, so that exp licit calculations relating to these singularities can be avoided. The modifications necessary to take care of the cases of a singular space curve, or a curve not in general position, are given. An appendix ske tches a proof of the result that the projection of a non-singular rati onal, non-planar space curve from any point is birational. (C) 1997 Pu blished by Elsevier Science B.V.