The EMS Publishing House is now EMS Press and has its new home at

Please find all EMS Press journals and articles on the new platform.

L’Enseignement Mathématique

Full-Text PDF (340 KB) | Metadata | Table of Contents | LEM summary
Online access to the full text of L’Enseignement Mathématique is restricted to the subscribers of the journal, who are encouraged to communicate their IP-address(es) to their agent or directly to the publisher at
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