Part of MS66 Approximation Theory, Geometric Modeling, and 
  Algebraic Geometry - Part II of III
Wachspress Varieties

Abstract. Wachspress Varieties

Eugene Wachspress introduced rational barycentric coordinates for 
convex polygons in R^2, which Warren generalized to all convex 
polytopes in R^d.  These Wachspress barycentric coordinates are 
the unique rational barycentric coordinates of minimal degree.   
The Wachspress coordinates of a polytope P in R^d define a map 
of projective d-space to a projective space spanned by the vertices 
of P whose image is a Wachspress variety.

In this talk, I will describe the Wachspress variety and its 
defining ideal, which is the ideal of algebraic relations among 
the Wachspress coordinates.   This is joint work with Corey Irving, 
Hal Schenck, and Greg Smith.

Authors

 Frank Sottile, Texas A&M University, USA, sottile@math.tamu.edu
 Corey Irving, Santa Clara University, USA, cirving@scu.edu
 Henry Schenck, University of Illinois, USA, schenck@math.uiuc.edu
 Gregory Smith, Queen's University, Canada, ggsmith@mast.queensu.ca