Implicitization techniques: a fruitful interaction between practitioners and algebraists

A. DICKENSTEIN

Kolympari, Creta

Congreso; SAGA Fall School; 2010

SAGA ITN Marie Curie

We will recall different algebraic techniques for the implicitization of rational surfaces, with an emphasis on the use of linear syzygies. The theoretical approach for this method uses rather sophisticated algebraic tecniques for its justification,  first introduced by Laurent Busé, Marc Chardin and Jean Pierre Jouanolou. Their work was inspired by the method of moving curves, introduced by Thomas Sederberg and Falai Chen. We will focus on exploiting the monomial structure of the polynomials defining the parametrization, following recent work with Nicolás Botbol and Marc Dohm, and we will present implementations in the free computer algebra system Macaulay2.