Tropical compactification

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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 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 , a toric variety , the compatification is tropical when the map

is faithfully flat and is proper.

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References

From left: Hannah Markwig, Aaron Bertram, and Renzo Cavalieri, 2012 at the MFO Markwig bertram cavalieri.jpg
From left: Hannah Markwig, Aaron Bertram, and Renzo Cavalieri, 2012 at the MFO
  1. 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.
  2. 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.