Real and Positive Tropicalizations of Symmetric Determinantal Varieties

Algebraic Combinatorics 2026 Open access

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Authors: Abeer Al Ahmadieh, May Cai, Josephine Yu
DOI: 10.5802/alco.462
Cited by: 0
References: 22

Abstract

We study real and positive tropicalizations of the varieties of low rank symmetric matrices over real or complex Puiseux series. We show that real tropicalization coincides with complex tropicalization for rank two and corank one cases. We also show that the two notions of positive tropicalization introduced by Speyer and Williams coincide for symmetric rank two matrices, but they differ for symmetric corank one matrices.

Fields of Study & Subjects

Polynomial and algebraic computation Algebraic Geometry and Number Theory Advanced Combinatorial Mathematics

Publication details

Journal / source
Algebraic Combinatorics
Volume
9
Issue
1
Pages
1–19
Publication date
3 March 2026
Language
EN