matroidRealizationSpaces

Code used in the paper Singular matroid realization spaces by Daniel Corey and Dante Luber. This code works with OSCAR version 0.12.1. Note: it may be essential to use this version of OSCAR. To ensure this, do the following. First, run julia --project=. in the terminal from the root of this project. Next, open julia and run the following:

julia> using Pkg
julia> Pkg.instantiate()

Functions and documentation

All new functions are in the src directory. The documentation is contained in the jupyter notebook functionDocumentation.ipynb. Note In the file src/matroid_realization.jl, some of these functions and the structure MatroidRealizationSpace were developed with Lukas Kühne, and will be incorporated in a later version of Oscar.

Smoothness of realization spaces

The code used to determine smoothness (and in some cases, irreducibility) may be found in the folders d3n9, d3n10, d3n11, d4n8, d4n9, where, e.g., d3n9 contains the data for rank $d=3$ matroids on $n=9$ elements. In each folder is a jupyter notebook that contains all instructions for the smoothness tests.

Singular realization spaces

The jupyter notebook matroids-3-12.ipynb contains code to verify that the $(3,12)$--matroid in section 4.2 has a singular realization space, as well as code used in Proposition 6.7 to verify that the coordinatewise valuation of the Plücker coordinates of the row spans of the matrices $C_1, C_2$ both equal the corank vector of this matroid.