Implicitization of tensor product surfaces with basepoints via residual resultants

A tensor product surface is the image of a rational map p P^1xP^1->P^3. Such surfaces arise in geometric modelling and in this context it is useful to know the implicit equation of the closure of the image. In this talk I will introduce a residual resultant for P^1xP^1 following Gelfand, Kapranov, Zelevinski and show that it can be computed using virtual projective resolutions. Afterwards I will explain how to use the residual resultant in P^1xP^1 to compute implicit equations of tensor product surfaces. Many examples and concrete computations will be presented.