Algebraic Matroids and Realizability of Tropical Varieties up to Scaling
Josephine Yu · arXiv (Cornell University) · 2015
We show that if the Bergman fan of a matroid $M$ is realizable as the ground set of the tropicalization of an ideal over a field $K$, then $M$ is an algebraic matroid over $K$. It follows that there are infinitely many Bergman fans that are not realizable as tropicalizations, with respect to any weight.