Set-theoretic generators of rational space curves

Authors:
Xiaohong Jia;Haohao Wang;Ron Goldman
Affiliations:
Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026, China and Department of Computer Science, The University of Hong Kong, Hong Kong, China;Department of Mathematics, Southeast Missouri State University, Cape Girardeau, MO 63701, United States;Computer Science Department, Rice University, 6100 Main Street, MS-132, Houston, TX 77251, United States
Venue:
Journal of Symbolic Computation
Year:
2010

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Abstract

We show how to calculate three low degree set-theoretic generators (i.e., algebraic surfaces) for all rational space curves of low degree (degree @?6) as well as for all higher degree rational space curves where at least one element of their @m-basis has degree 1 from a @m-basis of the parametrization. In addition to having low degree, at least two of these surface generators are always ruled surfaces. Whenever possible we also show how to compute two set-theoretic complete intersection generators for these rational space curves from a @m-basis of their parametrization.