G-2012-101
The Injectivity Modules of a Tropical Map
BibTeX reference
In [Wagneur, E., Linear Algebra and its Application, 435, 1786-1795, 2011], we show that any m
-dimensional tropical torsion module can be embedded in R_d
, with d≤m(m−1)
, and that m
-dimensional tropical torsion modules are classified by
a p
-parameter family, with p≤(m−1)[m(m−1)−1]
.
The aim of the paper is to revisit and extend some of these results by showing that - at least in the 3-dimensional case - the two upper bounds are tight. More precisely, we show that for m=3
, we can find tropical torsion modules which cannot be
embedded in R_d
for d<6
, and that all the p=2⋅(2⋅3−1)=10
parameters required for the unambiguous specification of the 3 generators of m
are necessary for the characterization of m
.
Published December 2012 , 10 pages
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G-2012-101.pdf (300 KB)