We also construct a sheaf on formula_7, called the “structure sheaf” as in the affine case, which makes it into a scheme. As in the case of the Spec construction there are many ways to proceed: the most direct one, which is also highly suggestive of the construction of regular functions on a projective variety in classical algebraic geometry, is the following. For any open set formula_21 of formula_7 (which is by definition a set of homogeneous prime ideals of "formula_1" not containing formula_24) we define the ring formula_25 to be the set of all functions