We understand tropical hypersurfaces and tropical linear spaces quite
well, on account of the fact that their combinatorial types are in
bijection with polyhedral subdivisions to which they're dual, of
respectively Newton polytopes and matroid polytopes. These are both
special cases of Chow polytopes, so it's natural to ask what we can
learn about general tropical varieties from Chow polytopes. I'll
discuss this question. I'll describe how Chow polytopes can lucidly
be obtained from tropical varieties by a certain Minkowski sum
operation, and I'll use this machinery to show the equivalence of the
intersection-theoretic and matroid-theoretic definitions of tropical
linear spaces.

Lecture #13905

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