Description:
This is the accompanying software package of the paper
"Cox rings of cubic surfaces and smooth Fano threefolds".
It implements the algorithms developed in
"Computing Cox rings"
to compute Cox rings of modifications.
This is a package for the computer algebra system Singular.
Features:
Given a modification \(X_2 \to X_1\) of projective varieties, e.g., a series
of blow ups, where
one of the Cox rings \(\mathcal{R}(X_i)\) is known, this package
provides procedures to obtain the other Cox ring.
This includes algorithms to
- verify finite generation of \(\mathcal{R}(X_i)\),
- verify a guess of generators for \(\mathcal{R}(X_i)\),
- produce a guess of generators for \(\mathcal{R}(X_2)\),
- present the new Cox ring by generators and relations.
Installation and download
-
Make sure you have Singular 3.1.6 or newer installed.
-
Download the file
compcox.lib.
-
Run Singular in the directory containing compcox.lib and load it
via the command LIB "compcox.lib";
If you use Singular 4.x, you first have to execute the line
LIB"gfanlib.so";
Note:
This is still under development.
Use it at your own risk. License: GNU GPL ver. 2 or 3 (at your option).