Loading...
Please wait, while we are loading the content...
Similar Documents
Reductive and unipotent actions of affine groups
| Content Provider | Semantic Scholar |
|---|---|
| Author | Walter, F. Alvaro, Rittatore |
| Copyright Year | 2014 |
| Abstract | We present a generalized version of classical geometric invariant theory \`a la Mumford where we consider an affine algebraic group $G$ acting on a specific affine algebraic variety $X$. We define the notions of linearly reductive and of unipotent action in terms of the $G$ fixed point functor in the category of $(G,\Bbbk [X])$--modules. In the case that $X=\{\star\}$ we recuperate the concept of lineraly reductive and of unipotent group. We prove in our "relative" context some of the classical results of GIT such as: existence of quotients, finite generation of invariants, Kostant--Rosenlicht's theorem and Matsushima's criterion. We also present a partial description of the geometry of such linearly reductive actions. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://arxiv.org/pdf/1406.4446v1.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
