More precisely, the existence of non-trivial automorphisms of the objects being classified makes it impossible to have a fine moduli space. However, it is often possible to consider a modified moduli problem of classifying the original objects together with additional data, chosen in such a way that the identity is the only automorphism respecting also the additional data. With a suitable choice of the rigidifying data, the modified moduli problem will have a (fine) moduli space "T", often described as a subscheme of a suitable Hilbert scheme or Quot scheme. The rigidifying data is moreover chosen so that it corresponds to a principal bundle with an algebraic structure group "G". Thus one can move back from the rigidified problem to the original by taking quotient by the action of "G", and the problem of constructing the moduli space becomes that of finding a scheme (or more general space) that is (in a suitably strong sense) the quotient "T"/"G" of "T" by the action of "G". The last problem, in general, does not admit a solution; however, it is addressed by the groundbreaking geometric invariant theory (GIT), developed by David Mumford in 1965, which shows that under suitable conditions the quotient indeed exists.