Tropicalisation of Conics Report

Title

Tropicalisation of Conics Report

Subject

Mathematics

Date

2025

Contributor

Xavier Gasper Ibrahim Adnan Khan

Abstract

We investigated the matroid of the degree-d Macaulay matrix of a conic polynomial, a problem with applications in tropical geometry. Employing graph-theoretic methods and Macaulay2 programs, we analysed the $0$-determinant submatrices of the Macaulay matrix satisfying the Fink-Giansiracusa condition. We uncovered a novel method for generating singular submatrices satisfying this condition, in arbitrary degree, through the embedding of singular minors from lower degrees.

Meta Tags

Tropical Geometry, Combinatorics, Linear Algebra

Files

Collection

Mathematics

Citation

Xavier Gasper, “Tropicalisation of Conics Report,” URSS SHOWCASE, accessed November 1, 2025, https://urss.warwick.ac.uk/items/show/909.