Bezout's Theorem and Implicitization

Friday, June 1, 2007 - 3:10pm - 3:40pm
EE/CS 3-180
Carlos D'Andrea (University of Barcelona)
This is a joint work with Martin Sombra.

The computation of the implicit equations of polynomial and rational parametrizations is always a hot topic in Computational Algebraic Geometry and CAGD. Recently, a lot of attention has been given to the computation of the Newton Polytope of the implicit equation, given the supports of the parametrization (sparse philosophy).

In this talk, we will show how the use of classical intersection theory in the torus can give us non-trivial information about this Newton Polytope. As an application of these results, we can give a complete description of the Newton Polytope of the implicit equation of a generic plane rational curve.