I was recently reading one of the papers of Kapranov on $\mathcal{M}\_{0,n}$ and he says that one can see it as a subvariety of the Hilbert scheme parametrizing all subschemes of a certain projective space. What is the precise definition of this Hilbert scheme? Why it is sure it exists? Is it in EGA somewhere or does anybody have a reference?



one "big" Hilbert scheme?
The construction is done in Geometry of Algebraic Curves by Arbarello et al.


