Algebraic matroids and set-theoretic realizability of tropical varieties

作者：Yu Josephine^*

来源：Journal of Combinatorial Theory - Series A, 2017, 147: 41-45.

DOI：10.1016/j.jcta.2016.11.007

• Algebraic matroids
• Tropical geometry
• Tropical varieties
• Bergman fans

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.

• 出版日期2017-4