# Contents

## Idea

Generally, given an action of a group on some space, then a stable point of the action is one whose stabilizer subgroup is a finite group. This means that the quotient stack restricted to the stable points is “tame” in that it is just an orbifold.

More specifically, in geometric invariant theory one gives criteria for (semi-)stability of points in projective varieties under the action of reductive groups. A central application here is to the construction of moduli stacks of (semi-)stable vector bundles, which are, roughly, the (semi-)stable points under the action of the gauge group.

A review of the definition of GIT-(semi-)stable points is in (Saiz 09, pp. 27-28). Review of (semi-)stable vector bundles as GIT-(semi-)stable points is in (Saiz 09, section 2.3).

## References

Review is in

For original references see at geometric invariant theory.

Created on July 14, 2014 at 05:28:33. See the history of this page for a list of all contributions to it.