Resumen de Compactifications of subvarieties of tori

Jenia Tevelev

• 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 $M_{0,n}\subset\overline{M}_{0,n}$ (and more generally log canonical models of complements of hyperplane arrangements) and compact quotients of Grassmannians by a maximal torus