Computing GIT-fans with symmetry and the Mori chamber decomposition of $overline {M}_{0,6}$

摘要

We propose an algorithm to compute the GIT-fan for torus actions on affine varieties with symmetries. The algorithm combines computational techniques from commutative algebra, convex geometry, and group theory. We have implemented our algorithm in the S INGULAR library GITFAN.LIB . Using our implementation, we compute the Mori chamber decomposition of  $ operatorname {Mov}(overline {M}_{0,6})$.