DefinitionDefinition: Literature-sourcedProof: Not applicablejudge pass (gpt-5.6-terra)audited 2026-09-06

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

projective space points

Definition

Fix an algebraically closed field $k$ . For $n \geq 0$ , define $P_{k}^{n} = (k^{n + 1} ∖ {0}) / \sim$ , where $a \sim b$ exactly when $b = λ a$ for some $λ \in k^{\times}$ . Write a class as $[a_{0} : \dots : a_{n}]$ . Thus $P_{k}^{0} = {[1]}$ .

Used by

inhomogeneous equation not projectively well defined Counterexample
morphism to projective space homogeneous coordinates Definition
projective algebraic set Definition
projective line two affine charts Example
homogeneous polynomial zero locus well defined Lemma
standard projective opens are affine spaces Lemma

Dependency tree · 0 levels

Nothing. This result depends on no other item in the library.

Sources

J. S. Milne, Algebraic Geometry, Chapter 6 (standard reference, not scraped)
Michael Artin, Algebraic Geometry, Chapter 3 (standard reference, not scraped)