Tropical linear spaces and tropical convexity
The electronic journal of combinatorics, Tome 22 (2015) no. 4
In classical geometry, a linear space is a space that is closed under linear combinations. In tropical geometry, it has long been a consensus that tropical varieties defined by valuated matroids are the tropical analogue of linear spaces. It is not difficult to see that each such space is tropically convex, i.e. closed under tropical linear combinations. However, we will also show that the converse is true: Each tropical variety that is also tropically convex is supported on the complex of a valuated matroid. We also prove a tropical local-to-global principle: Any closed, connected, locally tropically convex set is tropically convex.
DOI :
10.37236/5271
Classification :
52A07, 52A20, 52B40, 14N25
Mots-clés : tropical geometry, tropical convexity, linear spaces, matroids
Mots-clés : tropical geometry, tropical convexity, linear spaces, matroids
Affiliations des auteurs :
Simon Hampe 1
@article{10_37236_5271,
author = {Simon Hampe},
title = {Tropical linear spaces and tropical convexity},
journal = {The electronic journal of combinatorics},
year = {2015},
volume = {22},
number = {4},
doi = {10.37236/5271},
zbl = {1330.14099},
url = {http://geodesic.mathdoc.fr/articles/10.37236/5271/}
}
Simon Hampe. Tropical linear spaces and tropical convexity. The electronic journal of combinatorics, Tome 22 (2015) no. 4. doi: 10.37236/5271
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