Implicitization of surfaces via syzygies

Parameterized curves and surfaces are very common in Computer Aided Geometric Design and in this context it is important to obtain their implicit equations at a low computational cost. We will explain how to use syzygies to obtain implicit equations of parameterized surfaces. Implicitization algorithms via syzygies are more versatile and in many cases have faster running times than algorithms using Grobner bases and resultants. Our study will focus on the structure of the syzygies that determine the implicit equations for tensor product surfaces with basepoints.