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Algebraic Matroids and Set-theoretic Realizability of Tropical Varieties (1506.01427v2)
Published 3 Jun 2015 in math.CO and math.AG
Abstract: To each prime ideal in a polynomial ring over a field we associate an algebraic matroid and show that it is preserved under tropicalization. This gives a necessary condition for a tropical variety to be set-theoretically realizable from a prime ideal. We also show that there are infinitely many Bergman fans that are not set-theoretically realizable as the tropicalization of any ideal.
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