Universal Rational Parametrizations and Toric Varieties

Abstract

This note proves the existence of universal rational parametrizations. The description involves homogeneous coordinates on a toric variety coming from a lattice polytope. We first describe how smooth toric varieties lead to universal rational parametrizations of certain projective varieties. We give numerous examples and then discuss what happens in the singular case. We also describe rational maps to smooth toric varieties.

25 pages. To appear in the Procedings of the Workshop on Algebraic Geometry and Geometric Modeling, Vilnius, Lithuania, August 2002