Compactifications of subvarieties of tori

Details Compactifications of subvarieties of tori Compactifications of subvarieties of tori

2004-12-16

arxiv.org/abs/math/0412329v3

Mathematics

Algebraic Geometry

14 pages, submitted version

Scientific paper

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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