Tropical Positivity and Determinantal Varieties
Combinatorics
2022-05-31 v1 Algebraic Geometry
Abstract
We initiate the study of positive-tropical generators as positive analogues of the concept of tropical bases. Applying this to the tropicalization of determinantal varieties, we develop criteria for characterizing their positive part. We focus on the study of low-rank matrices, in particular matrices of rank 2 and 3. Moreover, in the case square-matrices of corank 1, we fully classify the signed tropicalization of the determinantal variety, even beyond the positive part.
Keywords
Cite
@article{arxiv.2205.14972,
title = {Tropical Positivity and Determinantal Varieties},
author = {Marie-Charlotte Brandenburg and Georg Loho and Rainer Sinn},
journal= {arXiv preprint arXiv:2205.14972},
year = {2022}
}