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 algebraic set

Definition

For homogeneous $T \subseteq k [x_{0}, \dots, x_{n}]$ , let $V_{+} (T) = {[a] \in P_{k}^{n} : F (a) = 0 for all F \in T}$ . A projective algebraic set is a set $V_{+} (T)$ ; write $V_{+} (J)$ for a homogeneous ideal. By convention $V_{+} (\emptyset) = P_{k}^{n}$ and $V_{+} ((x_{0}, \dots, x_{n})) = \emptyset$ .

Depends on

Used by

affine cone projective set Definition
degree projective hypersurface Definition
homogeneous coordinate ring Definition
projective closure affine set Definition
projective variety classical Definition
Closed projective embedding from a radical homogeneous ideal Theorem
projective zariski topology Theorem

Dependency tree · two levels

5 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

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