Geometric invariant theory

Summary

Geometric invariant theory, or GIT, is a method for building quotients of algebraic varieties by actions of reductive groups. It replaces the orbit space, which is often badly behaved, by the spectrum or the Proj of a ring of invariants. To get a good quotient one throws away the unstable points and keeps the semistable ones. David Mumford developed the theory to construct moduli spaces, such as the moduli of curves and of vector bundles.