2015/06/03 by Josephine Yu, Yu, Josephine · 1 citation
Computer Science · Mathematics · #05B35 #14T05 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1506.01427
openalex publication_date 2015/06/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.