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 of square-matrices of corank 1, we fully classify the signed tropicalization of the determinantal variety, even beyond the positive part.
| Original language | English |
|---|---|
| Pages (from-to) | 999-1040 |
| Number of pages | 42 |
| Journal | Algebraic Combinatorics |
| Volume | 6 |
| Issue number | 4 |
| Early online date | 29 Aug 2023 |
| DOIs | |
| Publication status | Published - 2023 |
Keywords
- bicolored phylogenetic trees
- Birkhoff polytope
- determinantal varieties
- positive-tropical generators
- signed tropicalization