Compactifications of subvarieties of tori

Abstract. We study compactifications of subvarieties of algebraic tori defined by imposing a suffi-ciently 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 M0,n ⊂ M0,n (and more generally log canonical models of complements of hyperplane arrangements) and compact quotients of Grassmannians by a maximal torus. 1. Introduction and statement of results. Let X be a connected closed subvariety of an algebraic torus T over an algebraically closed field k. It is natural to consider compactifications X defined as closures of X in various toric varieties P of T. In this paper we address the following question: how nice could X possibly be? Consider the multiplication ma