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Licensed Unlicensed Requires Authentication Published by De Gruyter July 20, 2012

Dressians, tropical Grassmannians, and their rays

Sven Herrmann, Michael Joswig and David E Speyer
From the journal Forum Mathematicum

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 Δ(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).

MSC: 52B40; 14P99

Funding source: German Academic Exchange Service (DAAD)

Award Identifier / Grant number: Postdoc-Program

Funding source: DFG

Award Identifier / Grant number: Priority Program 1489 Experimental Methods in Algebra, Geometry and Number Theory

We are indebted to an anonymous referee for several very helpful suggestions.

Received: 2012-3-18
Revised: 2012-5-29
Published Online: 2012-7-20
Published in Print: 2014-11-1

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