2010/10/19 by Kristin Shaw, Shaw, Kristin M. · 3 citations
Computer Science · Mathematics · #14C17 #14T05 #52B40 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.1010.3967
openalex publication_date 2010/10/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We construct an intersection product on tropical cycles contained in the Bergman fan of a matroid. To do this we first establish a connection between the operations of deletion and restriction in matroid theory and tropical modifications as defined by Mikhalkin. This product generalises the product of Allermann and Rau, and Allermann and also provides an alternative procedure for intersecting cycles which is not based on intersecting with Cartier divisors. Also, we simplify the definition in the case of one dimensional fan cycles in two dimensional matroidal fans and given an application of the intersection product to realisability questions in tropical geometry.