Dimension computations for tropical determinantal varieties and prevarieties

Abstract

This paper proves that when the $r\times r$ minors of an $m\times n$ matrix of indeterminates are not a tropical basis then the tropical prevariety has greater dimension than the tropical variety. It proves the same for the $r\times r$ minors of an $n\times n$ symmetric matrix of indeterminates when r > 4.

25 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:2112.14945, arXiv:2201.01028