 For example, if a few points have non-trivial stabilisers, then the categorical quotient will not exist among schemes.In the same way, moduli spaces of curves, vector bundles, or other geometric objects are often best defined as stacks instead of schemes.Constructions of moduli spaces often proceed by first constructing a larger space parametrizing the objects in question, and then quotienting by group action to account for objects with automorphisms which have been overcounted.