2020/03/30 by Dominik Bendle, Bendle, Dominik, Boehm, Janko +4
Computer Science · Mathematics · #14M15 #14Q15 #14T15 #52B15 #68W10 #68W30 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #FOS: Computer and information sciences #FOS: Mathematics #Polynomial and algebraic computation #Symbolic Computation (cs.SC) #Tensor decomposition and applications
paper · pdf · doi:10.48550/arxiv.2003.13752
openalex publication_date 2020/03/30 · openalex created_date 2020/04/10 · openalex updated_date 2026/07/28
In this article, we present a massively parallel framework for computing tropicalizations of algebraic varieties which can make use of finite symmetries. We compute the tropical Grassmannian TGr0(3,8), and show that it refines the 15-dimensional skeleton of the Dressian Dr(3,8) with the exception of 23 special cones for which we construct explicit obstructions to the realizability of their tropical linear spaces. Moreover, we propose algorithms for identifying maximal-dimensional tropical cones which belong to the positive tropicalization. These algorithms exploit symmetries of the tropical variety even though the positive tropicalization need not be symmetric. We compute the maximal-dimensional cones of the positive Grassmannian TGr+(3,8) and compare them to the cluster complex of the classical Grassmannian Gr(3,8).