Tropical Compactification

In algebraic geometry, a tropical compactification is a compactification ( projective completion) of a subvariety of an algebraic torus, introduced by Jenia Tevelev. 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 compatification arises when trying to make compactifications as "nice" as possible. For a torus $T$, a toric variety $\mathbb$, the compatification $\bar$ is tropical when the map
:$\Phi: T \times \bar \to \mathbb,\ (t,x) \to tx$
is faithfully flat and $\bar$ is proper.

See also

*Tropical geometry
*GIT quotient
* Chow quotient
* Toroidal embedding

References

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Compactification

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