Compactifications of subvarieties of tori

Abstract

We study compactifications of subvarieties of algebraic tori defined by imposing a sufficiently fine polyhedral structure on their non-archimedean amoebas. These compactifications have many nice properties, for example any k boundary divisors intersect in codimension k. We consider some examples including $M_{0,n}\subset {\bar{M}}_{0,n}$ (and more generally log canonical models of complements of hyperplane arrangements) and compact quotients of Grassmannians by a maximal torus.

14 pages, submitted version

References in corpus (3)

• Matroid polytopes, nested sets and Bergman fans
• Chow Quotients of Grassmannians II
• The Tropical Grassmannian