Seminar Algebra and Geometry: Marc Chardin (Institut Mathématique de Jussieu, Paris)

Torsion in the symmetric algebra and images of rational maps

In this lecture, I will present a way of computing the image of a  rational map using a free resolution of the symmetric algebra. In this setting, the  method was initiated by Jean-Pierre Jouanolou, and further developed by him, by Laurent  Busé and by myself. The origin of this method is the work of people in Geometric  Modeling, motivated by a simple question: how to represent the  intersection of two surfaces parametrized by rational functions?

Their approach was first put on firm mathematical bases by David Cox and several collaborators. The key  point in this approach is to control the torsion in the symmetric algebra. This is performed using a construction of Herzog, Simis and Vasconcelos, that gives information on the equations of Rees algebras.

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