The Proj construction is a fundamental tool of scheme theory in algebraic geometry, serving as the projective counterpart to the spectrum-of-a-ring construction used to build affine schemes. It takes a graded ring, one with a direct sum decomposition indexed by the non-negative integers, and produces a projective scheme by collecting the homogeneous prime ideals that do not contain every positive-degree element, then equipping this set with a Zariski topology and a structure sheaf. Unlike the affine spectrum construction, the Proj construction is not functorial in the same straightforward way.
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1. Proj Construction (Wikipedia)
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In algebraic geometry, Proj is a construction analogous to the spectrum-of-a-ring construction of affine schemes, which produces objects with the typical properties of projective spaces and projective varieties.
In Branch: Algebraic Geometry, Lead sentence
In algebraic geometry, Proj is a construction analogous to the spectrum-of-a-ring construction of affine schemes, which produces o
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