DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-5.6-terra)audited 2026-09-09

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.

A classical affine variety

Definition

Over an algebraically closed field $k$ , a classical affine variety is a nonempty affine algebraic set $X \subseteq k^{n}$ which is irreducible in its Zariski topology: if $X = C \cup D$ with $C, D$ closed in $X$ , then $C = X$ or $D = X$ . The empty algebraic set is not a variety; a singleton, including $k^{0}$ , is irreducible. This convention reserves “algebraic set” for the possibly reducible or empty case.

Sources

Source comparison: Milne, Algebraic Geometry, v6.10, §2h p. 45. Conventions here distinguish arbitrary affine algebraic sets from nonempty irreducible varieties.

Depends on

Used by

Dependency tree · two levels

13 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 v6.10, §2h p. 45 (standard reference, not scraped)