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In algebraic geometry, a tropical compactification is a compactification of a subvariety of an algebraic torus, introduced by Jenia Tevelev. Given an algebraic torus and a connected closed subvariety of that torus, a compatification of the subvariety is defined as a closure of it in a toric variety of the original torus. The concept of a tropical compatification arises when trying to make compactifications as "nice" as possible. For a torus T {\displaystyle T} , a toric variety P {\displaystyle \mathbb {P} } , the compatification X ¯ {\displaystyle {\bar {X}}} is tropical when the map
is faithfully flat and X ¯ {\displaystyle {\bar {X}}} is proper.
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