In algebraic geometry, a tropical compactification is a compactification (projective completion) of a subvariety of an algebraic torus, introduced by Jenia Tevelev.[1][2] Given an algebraic torus and a connected closed subvariety of that torus, a compactification of the subvariety is defined as a closure of it in a toric variety of the original torus. The concept of a tropical compactification arises when trying to make compactifications as "nice" as possible. For a torus and a toric variety , the compactification is tropical when the map
is faithfully flat and is proper.
^Tevelev, Jenia (2007-08-07). "Compactifications of subvarieties of tori". American Journal of Mathematics. 129 (4): 1087–1104. arXiv:math/0412329. doi:10.1353/ajm.2007.0029. ISSN 1080-6377.
^Brugallé, Erwan; Shaw, Kristin (2014). "A Bit of Tropical Geometry". The American Mathematical Monthly. 121 (7): 563–589. arXiv:1311.2360. doi:10.4169/amer.math.monthly.121.07.563. JSTOR 10.4169/amer.math.monthly.121.07.563.
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