Kristian Ranestad

Title: Projective geometry of Wachspress coordinates

Abstract: 
There is a unique curve of minimal degree through the points of intersection of nonadjacent 
edges of a polygon in the plane. Wachspress used this fact in a generalisation of barycentric 
coordinates with reference to a convex polygon. Let P be a polytope in n-space, let H_P be the 
hyperplane arrangement defined by the facets of P. I shall report on ongoing work with Kathlen Kohn, 
where we show that if H_P is simple, there is a unique hypersurface of minimal degree that contains 
all linear spaces that are intersections of hyperplanes in H_P and do not contain any face of P.
We apply the result to give constructions of hypersurfaces with singularities along singular parts 
of H_P, whose minimal desingularization have a unique canonical divisor.