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We establish a natural and geometric 1-1 correspondence between projective toric varieties of dimension and horofunction compactifications of 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, Toric varieties vs. horofunction compactifications of polyhedral norms. Enseign. Math. 63 (2017), no. 3, pp. 375–401DOI 10.4171/LEM/63-3/4-6