TorDiv: Maple package on toric geometry and geometric invariant theory. 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.

Keywords for this software

Anything in here will be replaced on browsers that support the canvas element