Detecting tropical defects of polynomial equations

Görlach, Paul; Ren, Yue; Sommars, Jeff

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.

Citation

Görlach, P., Ren, Y., & Sommars, J. (2021). Detecting tropical defects of polynomial equations. Journal of Algebraic Combinatorics, 53(1), 31-47. https://doi.org/10.1007/s10801-019-00916-4

• Journal Article Type: Article
• Acceptance Date: Oct 4, 2019
• Online Publication Date: Nov 6, 2019
• Publication Date: 2021-02
• Deposit Date: May 16, 2023
• Journal: Journal of Algebraic Combinatorics
• Print ISSN: 0925-9899
• Electronic ISSN: 1572-9192
• Publisher: Springer
• Peer Reviewed: Peer Reviewed
• Volume: 53
• Issue: 1
• Pages: 31-47
• DOI: https://doi.org/10.1007/s10801-019-00916-4
• Public URL: https://durham-repository.worktribe.com/output/1174908