JournalslemVol. 63, No. 3/4pp. 375–401

Toric varieties vs. horofunction compactifications of polyhedral norms

  • Lizhen Ji

    University of Michigan, Ann Arbor, USA
  • Anna-Sofie Schilling

    Universität Heidelberg, Germany
Toric varieties vs. horofunction compactifications of polyhedral norms cover
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Abstract

We establish a natural and geometric 1-1 correspondence between projective toric varieties of dimension nn and horofunction compactifications of Rn\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.

Cite this article

Lizhen Ji, Anna-Sofie Schilling, Toric varieties vs. horofunction compactifications of polyhedral norms. Enseign. Math. 63 (2017), no. 3, pp. 375–401

DOI 10.4171/LEM/63-3/4-6