Algebraic matroids and set-theoretic realizability of tropical varieties

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:147

Article

Yu, Josephine¹ 

[1] Georgia Inst Technol, Sch Math, Atlanta, GA 30332 USA

关键词: Algebraic matroids;    Tropical geometry;    Tropical varieties;    Bergman fans;   

DOI  :  10.1016/j.jcta.2016.11.007

来源: Elsevier

【 摘 要 】

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. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

Free