Variations of GIT quotients package v0.6.13

Abstract

This software package is a complement to the articles Moduli of cubic surfaces and their anticanonical divisors and Variations of geometric invariant quotients for pairs, a computational approach, both available in the Arxiv. The software package implements a series of algorithms for the study of variations of Geometric Invariant Theory (GIT) quotients of pairs formed by a hypersurface in projective space of dimension n and degree d and a hyperplane embedded in the same projective space. Given a dimension n and a degree d, the code finds all relevant one-parameter subgroups which determine all the GIT quotients for these pairs. In addition, it finds a finite list of candidate 'walls' in the wall-chamber decomposition studied by Dolgachev-Hu and Thaddeus. Furthermore, for each prospective chamber and wall it finds all maximal orbits of non stable and strictly semistable pairs, as well as minimal closed orbits of strictly semistable pairs in terms of families of pairs defined by monomials with non-zero coefficients. Finally, it runs through all the list of prospective chambers and walls eliminating 'false walls' for which the GIT quotient is detected not to vary. Further details can be found at the article Variations of geometric invariant quotients for pairs, a computational approach. The full worked out output for cubic surfaces and hyperplanes, as reflected in Moduli of cubic surfaces and their anticanonical divisors, is attached as a text file. The sotware package is implemented as a Python 2.7 package and it requires several additional libraries to run which are all detailed in Installation file. The package has been thoroughly tested for Windows and it may work on Unix-based platforms with extra work.