for questions on geometric invariant theory (or GIT), including stability criteria and symplectic quotients.
Geometric invariant theory (or GIT) is a theoretical basis for the formation of quotients of algebraic varieties by actions of groups, developed in the 1960s by David Mumford. One of the key new ingredients in GIT is the fine analysis of stability for orbits. GIT quotient varieties are formed by removing non-stable orbits, since they would produce non-separable orbit spaces. GIT is often used to construct and analyze moduli spaces, and the theory has been extended beyond algebraic geometry, e.g., to symplectic geometry.