Deligne-Mumford stack

A Deligne-Mumford stack is a space that ``locally has the structure of a variety modulo a finite group.'' The stackiness comes from remembering this presentation, in a manner similar to the definition of an orbifold in usual topology. Many moduli problems are naturally represented by D-M stacks and not by schemes or varieties (for instance, they were defined to handle the moduli functor of stable curves).