On the stack of 0-dimensional coherent sheaves: structural aspects

Let X be a quasiprojective scheme. In this expository note we collect a series of useful structural results on the stack Cohⁿ(X) parametrising $0$-dimensional coherent sheaves of length n over X. For instance, we discuss its functoriality (in particular its behaviour along \'etale maps), the support morphism to Symⁿ(X), and its relationship with the Quot scheme of points QuotX( E,n) for fixed E∈ Coh(X).