Detecting tropical defects of polynomial equations
Algebraic Geometry
2019-11-12 v2 Symbolic Computation
Abstract
We introduce the notion of tropical defects, certificates that a system of polynomial equations is not a tropical basis, and provide two algorithms for finding them in affine spaces of complementary dimension to the zero set. We use these techniques to solve open problems regarding del Pezzo surfaces of degree 3 and realizability of valuated gaussoids on 4 elements.
Cite
@article{arxiv.1809.03350,
title = {Detecting tropical defects of polynomial equations},
author = {Paul Görlach and Yue Ren and Jeff Sommars},
journal= {arXiv preprint arXiv:1809.03350},
year = {2019}
}
Comments
Changes: improved presentation in Section 2. To appear in Journal of Algebraic Combinatorics