CONICET | Buscador de Institutos y Recursos Humanos

We unveil in concrete terms the general machinery of the syzygy- based algorithms for the implicitization of rational surfaces in terms of the monomials in the polynomials defining the parametrization, following and ex- panding our joint article with M. Dohm. These algebraic techniques, based on the theory of approximation complexes due to J. Herzog, A, Simis and W. Vas- concelos, were introduced for the implicitization problem by J.-P. Jouanolou, L. Busé, and M. Chardin. Their work was inspired by the practical method of moving curves, proposed by T. Sederberg and F. Chen, translated into the lan- guage of syzygies by D. Cox. Our aim is to express the theoretical results and resulting algorithms into very concrete terms, avoiding the use of the advanced homological commutative algebra tools which are needed for their proofs.