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Abstract:
Subvarieties of algebraic tori have many unexpected geometric properties that makes them similar to subvarieties of Abelian varieties. For example, they are their own logcanonical models
(conjectured by Miles Reid). One can study them using a combination
of Mori theory and tropical geometry. This leads, for example,
to the complete description of the modular compactification
of the moduli space of cubic surfaces marked by 27 lines completely
analogous to the moduli space of stable rational curves
with n marked points (joint with Paul Hacking and Sean Keel).
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