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arXiv · 1705.00910

Canonical decomposition of a difference of convex sets

Ana María Botero
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Abstract

Let $N$ be a lattice of rank $n$ and let $M = N^{\vee}$ be its dual lattice. In this note we show that given two compact, bounded, full-dimensional convex sets $K_1 \subseteq K_2 \subseteq M_{\R} \coloneqq M \otimes_{\Z} \R$, there is a canonical convex decomposition of the difference $K_2 \setminus K_1$ and we interpret the volume of the pieces geometrically in terms of intersection numbers of toric $b$-divisors.

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Ana María Botero. 2017-05-02. Canonical decomposition of a difference of convex sets. https://arxiv.org/abs/1705.00910

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