Compactifications of Subvarieties of Tori Jenia Tevelev

  title={Compactifications of Subvarieties of Tori Jenia Tevelev},
  author={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 M0,n ⊂ M0,n (and more generally log canonical models of complements of hyperplane arrangements) and compact quotients of Grassmannians by a maximal torus. 

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