Canonical decomposition of a difference of convex sets

Ana M. Botero
2019 Algebraic Combinatorics  
Let N be a lattice of rank n and let M = N ∨ be its dual lattice. In this article we show that given two closed, bounded, full-dimensional convex sets K 1 ⊆ K 2 ⊆ M R := M ⊗ Z R, there is a canonical convex decomposition of the difference K 2 int(K 1 ) and we interpret the volume of the pieces geometrically in terms of intersection numbers of toric b-divisors.
doi:10.5802/alco.55 fatcat:ct4oayvrxngwbjznulk5kq4q2i