2024/07/02 by Juan Bosco Frías-Medina, Frías-Medina, Juan Bosco, Timothy Magee +1
Computer Science · #13F60 #14M99 #51M20 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #Computational Geometry and Mesh Generation #FOS: Mathematics #Primary: 52A01 #Secondary: 14J33
paper · pdf · doi:10.48550/arxiv.2407.02427
openalex publication_date 2024/07/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We develop the fundamentals of a new theory of convex geometry -- which we call "broken line convex geometry". This is a theory of convexity where the ambient space is the rational tropicalization of a cluster variety, as opposed to an ambient vector space. In this theory, line segments are replaced by broken line segments, and we adopt the notion of convexity in [CMN21]. We state and prove broken line convex geometry versions of many standard results from usual convex geometry.