Mumford’s geometric invariant theory (GIT) provides a method for constructing quotient varieties for linear actions of reductive groups on projective varieties. The GIT quotient depends on the choice of linearization for the group action, and this dependence was described using ‘variation of GIT’ (VGIT) by Thaddeus and Dolgachev & Hu in the 1990s. GIT has been extended to non-reductive actions; many of the nice features of classical GIT fail in general, but are satisfied given the extra data of a graded linearization for an action of a linear algebraic group with graded unipotent radical. The aim of this talk is to describe this picture and a version of VGIT which applies to it (joint work with Gergely Berczi and Joshua Jackson).
This video is part of Harvard University‘s conference JDG 2017.
