Geodesic
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, Tome 2 (2019) no. 4, pp. 585-602

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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.

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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
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Botero, Ana M. Canonical decomposition of a difference of convex sets. Algebraic Combinatorics, Tome 2 (2019) no. 4, pp. 585-602. doi: 10.5802/alco.55

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