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arXiv · 1705.07599

Toric Varieties vs. Horofunction Compactifications of Polyhedral Norms

Lizhen Ji·Anna-Sofie Schilling
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Abstract

We establish a natural and geometric 1-1 correspondence between projective toric varieties of dimension $n$ and horofunction compactifications of $\mathbb{R}^n$ with respect to rational polyhedral norms. For this purpose, we explain a topological model of toric varieties. Consequently, toric varieties in algebraic geometry, normed spaces in convex analysis, and horofunction compactifications in metric geometry are directly and explicitly related.

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Lizhen Ji, Anna-Sofie Schilling. 2017-05-22. Toric Varieties vs. Horofunction Compactifications of Polyhedral Norms. https://arxiv.org/abs/1705.07599

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