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L’Enseignement Mathématique


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Volume 63, Issue 3/4, 2017, pp. 375–401
DOI: 10.4171/LEM/63-3/4-6

Published online: 2018-09-03

Toric varieties vs. horofunction compactifications of polyhedral norms

Lizhen Ji[1] and Anna-Sofie Schilling[2]

(1) University of Michigan, Ann Arbor, USA
(2) Universität Heidelberg, Germany

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.

Keywords: Toric varieties, horofunctions, compactifications

Ji Lizhen, Schilling Anna-Sofie: Toric varieties vs. horofunction compactifications of polyhedral norms. Enseign. Math. 63 (2017), 375-401. doi: 10.4171/LEM/63-3/4-6