It is frequently the case that interesting geometric objects come equipped with many natural automorphisms. This in particular makes the existence of a fine moduli space impossible (intuitively, the idea is that if "L" is some geometric object, the trivial family "L" × [0,1] can be made into a twisted family on the circle S1 by identifying "L" × {0} with "L" × {1} via a nontrivial automorphism. Now if a fine moduli space "X" existed, the map S1 → "X" should not be constant, but would have to be constant on any proper open set by triviality), one can still sometimes obtain a coarse moduli space. However, this approach is not ideal, as such spaces are not guaranteed to exist, they are frequently singular when they do exist, and miss details about some non-trivial families of objects they classify.