Detecting tropical defects of polynomial equations

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.

arXiv commentChanges: improved presentation in Section 2. To appear in Journal of Algebraic Combinatorics

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