2019/12/03 by Hill, Cvetelina, Lamboglia, Sara, Simon, Faye Pasley
#Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Metric Geometry (math.MG)
paper · doi:10.48550/arxiv.1912.01253
In this paper we focus on the tropical convex hull of convex sets and polyhedral complexes. We give a vertex description of the tropical convex hull of a line segment and a ray. %in \RRn+1/\RR1. Next we show that tropical convex hull and ordinary convex hull commute in two dimensions and characterize tropically convex polyhedra in any dimension. %ℝ3/\mathbb R1. Finally we show that the dimension of a tropically convex fan depends on the coordinates of its rays and give a lower bound on the degree of a fan tropical curve using only tropical techniques.