This repository contains the auxiliary code to the paper Discrete Geometry of Cox Rings of blow-ups of
The Arxiv identifier is 2208.05258.
We prove quadratic generation for the ideal of the Cox ring of
the blow-up of
The helper_functions.jl and cox_generators.jl contains auxiliary code for the main functions in is_khovanskii.jl. This is a quick example on how to use the code in a julia terminal:
julia> KS, (t,z...)=PolynomialRing(QQ, ["t",["z[$i]" for i in 1:7]...]);
julia> P=[t^59 t^44 t^79 t^20 t^12 t^81 t^36; t^8 t^72 t^49 t^39 t^58 t^23 t^64; t^44 t^58 t^12 t^52 t^57 t^49 t^51; t^25 t^23 t^60 t^72 t^45 t^51 t^6];
julia> bool,_,_=generalposition_monomeric_check(P);
julia> bool
true
The necessary code for the proof of Theorem 12 is contained in the tutorial.jl jupyter notebook. The file Lemma22.ipynb contains the code necessary for the proof of Corollary 22.
Mara Belotti, Marta Panizzut. Discrete geometry of Cox rings of blow-ups of