Tropical compactification

Template:Short description 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 compactification arises when trying to make compactifications as "nice" as possible. For a torus $T$ and a toric variety $\mathbb{P}$, the compactification $\overline{X}$ is tropical when the map

$\mathrm{\Phi }:T\times \overline{X}\to \mathbb{P},(t,x)\to tx$

is faithfully flat and $\overline{X}$ is proper.

See also

• Tropical geometry
• GIT quotient
• Chow quotient
• Toroidal embedding

References

From left: Hannah Markwig, Aaron Bertram, and Renzo Cavalieri, 2012 at the MFO

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