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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 dm(m1), and that m-dimensional tropical torsion modules are classified by a p-parameter family, with p(m1)[m(m1)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(231)=10 parameters required for the unambiguous specification of the 3 generators of m are necessary for the characterization of m.

, 10 pages

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