## TorDiv - A Maple Package

### on Toric Varieties and Geometric Invariant Theory

Current version: 1.4 (February 23, 2010),
Copyright © 2010, F. Berchtold, J. Hausen, S. Keicher, R. Vollmert, M. Widmann
### Description

TorDiv is a Maple Package, distributed under the
GNU General Public License.
It comprises functions on toric varieties and,
as this is a strongly related subject, geometric invariant theory
of linear torus actions. The aim is to provide an easy-to-use
working environment for study and discussion of (advanced) examples.
Toric varieties are entered in terms of their defining
fan in the lattice of one parameter subgroups, or, equivalently,
by their defining bunch of cones in the divisor class group.
Torus actions are entered as lists of weight vectors.
TorDiv then offers among others the following functions:

- Conversion from defining fan to defining bunch of cones and vice versa.
- Computation of the invariant Cartier divisors and the Picard group.
- Computation of the moving cone, the numerically effective cone, and the
ample cone.
- Computation of Cox's and Kajiwara's quotient presentation.
- Tests for quasiprojectivity and divisoriality.
- Tests for the Gorenstein and Fano properties.
- Computation of sets of semistable points and their quotients.
- Test for existence of a good quotient.
- Computations of GIT-fans and GIT-limits.
- Computations of polyhedral divisors.

### Software Requirements

The TorDiv package requires Maple, Version 8 or higher,
and the Maple package
convex
by
Matthias Franz.
### Installation

For a quick installation of TorDiv,
download by clicking the files
TorDiv14.ind
and
TorDiv14.lib,
and put them into your personal Maple library
directory. Then, similar to any other Maple package,
TorDiv is activated via the Maple command "with(TorDiv14);".
For more information, see
README.

### Beta version

TorDiv 1.5: download by clicking the files
TorDiv15.ind
and
TorDiv15.lib.
### Documentation

There is a detailed documentation on the TorDiv 1.4 package:
manual.pdf.
It contains some mathematical background, descriptions of all
functions of the TorDiv package, and an example for each function.

Mathematisches Institut,
Universität
Tübingen,
updated: March 2012