11 research outputs found
Computing the GIT-fan
We present an algorithm to compute the GIT-fan of algebraic torus actions on
affine varieties.Comment: minor changes; to appear in Internat. J. Algebra Compu
A software package for Mori dream spaces
Mori dream spaces form a large example class of algebraic varieties,
comprising the well known toric varieties. We provide a first software package
for the explicit treatment of Mori dream spaces and demonstrate its use by
presenting basic sample computations. The software package is accompanied by a
Cox ring database which delivers defining data for Cox rings and Mori dream
spaces in a suitable format. As an application of the package, we determine the
common Cox ring for the symplectic resolutions of a certain quotient
singularity investigated by Bellamy/Schedler and Donten-Bury/Wi\'sniewski.Comment: 11 pages, minor changes, to appear in LMS Journal of Computation and
Mathematic
Computation of GIT quotients of semisimple groups
We describe three algorithms to determine the stable, semistable, and
torus-polystable loci of the GIT quotient of a projective variety by a
reductive group. The algorithms are efficient when the group is semisimple. By
using an implementation of our algorithms for simple groups, we provide several
applications to the moduli theory of algebraic varieties, including the
K-moduli of algebraic varieties, the moduli of algebraic curves and the Mukai
models of the moduli space of curves for low genus. We also discuss a number of
potential improvements and some natural open problems arising from this work.Comment: 32 pages, 3 figures. 1 tabl