Real and Positive Tropicalizations of Symmetric Determinantal Varieties
Algebraic Geometry
2024-09-27 v1 Combinatorics
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.
Keywords
Cite
@article{arxiv.2409.17462,
title = {Real and Positive Tropicalizations of Symmetric Determinantal Varieties},
author = {Abeer Al Ahmadieh and May Cai and Josephine Yu},
journal= {arXiv preprint arXiv:2409.17462},
year = {2024}
}