# ALGEBRAIC COMBINATORICS

Canonical decomposition of a difference of convex sets
Algebraic Combinatorics, Volume 2 (2019) no. 4, pp. 585-602.

Let $N$ be a lattice of rank $n$ and let $M={N}^{\vee }$ be its dual lattice. In this article we show that given two closed, bounded, full-dimensional convex sets ${K}_{1}\subseteq {K}_{2}\subseteq {M}_{ℝ}:=M{\otimes }_{ℤ}ℝ$, there is a canonical convex decomposition of the difference ${K}_{2}\setminus \text{int}\left({K}_{1}\right)$ and we interpret the volume of the pieces geometrically in terms of intersection numbers of toric $b$-divisors.

Revised:
Accepted:
Published online:
DOI: 10.5802/alco.55
Classification: 52A22,  14M25,  14C17
Keywords: convex geometry, toric geometry, intersection theory
Botero, Ana M. 1

1 University of Regensburg Dept. of mathematics Universitätsstr. 31 93053 Regensburg, Germany
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Botero, Ana M. Canonical decomposition of a difference of convex sets. Algebraic Combinatorics, Volume 2 (2019) no. 4, pp. 585-602. doi : 10.5802/alco.55. https://alco.centre-mersenne.org/articles/10.5802/alco.55/

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