DRESSIANS, TROPICAL GRASSMANNIANS, AND THEIR RAYS
Sven C. Herrmann, Michael Joswig, David E Speyer · 2016
Abstract. The Dressian Dr(k, n) parametrizes all tropical linear spaces, and it carries a natural fan structure as a subfan of the secondary fan of the hypersimplex ∆(k, n). We explore the combinatorics of the rays of Dr(k, n), that is, the most degenerate tropical planes, for arbitrary k and n. This is related to a new rigidity concept for configurations of n − k points in the tropical (k−1)-torus. Additional conditions are given for k = 3. On the way, we compute the entire fan Dr(3, 8). 1.