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no. 4
Canonical decomposition of a difference of convex sets
Botero, Ana M.1
1 University of Regensburg Dept. of mathematics Universitätsstr. 31 93053 Regensburg, Germany
Algebraic Combinatorics, Volume 2 (2019) no. 4, pp. 585-602.

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.

Received:
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
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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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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