Whenever there is an embedding of a scheme formula_1 into the universal projective space formula_2, the embedding is given by a line bundle formula_3 and formula_4 sections formula_5 which all don't vanish at the same time. This means, given a pointformula_6there is an associated pointformula_7given by the compositionsformula_8Then, two line bundles with sections are equivalentformula_9iff there is an isomorphism formula_10 such that formula_11. This means the associated moduli functor formula_12sends a scheme formula_1 to the setformula_14Showing this is true can be done by running through a series of tautologies: any projective embedding formula_15 gives the globally generated sheaf formula_16 with sections formula_17. Conversely, given an ample line bundle formula_3 globally generated by formula_4 sections gives an embedding as above.