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Compactifications of subvarieties of tori

Jenia Tevelev
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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.

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Jenia Tevelev. 2005-08-21. Compactifications of subvarieties of tori. https://arxiv.org/abs/math/0412329

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