Algebraic Matroids and Set-theoretic Realizability of Tropical Varieties
Combinatorics
2016-08-12 v2 Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.1506.01427,
title = {Algebraic Matroids and Set-theoretic Realizability of Tropical Varieties},
author = {Josephine Yu},
journal= {arXiv preprint arXiv:1506.01427},
year = {2016}
}
Comments
4 pages. Minor revisions and changes to the title and abstract. To appear in JCTA