Tropical positivity and determinantal varieties

被引：4

作者：

Brandenburg, Marie-Charlotte ^{[1
]}

Loho, Georg ^{[2
]}

Sinn, Rainer ^{[3
]}

机构：

[1] Max Planck Inst Math Sci, Inselstr 22, D-04103 Leipzig, Germany

[2] Univ Twente, Drienerlolaan 5, NL-7522 NB Enschede, Netherlands

[3] Univ Leipzig, Augustuspl 10, D-04109 Leipzig, Germany

来源：

ALGEBRAIC COMBINATORICS | 2023年 / 6卷 / 04期

关键词：

signed tropicalization; positive-tropical generators; determinantal varieties; Birkhoff; polytope; bicolored phylogenetic trees; COLLINEAR POINTS; SPACE; MATRIX; MINORS;

D O I：

10.5802/alco.286

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：999 / 1040

页数：43

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