DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedaudited 2026-09-07

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.

Incidence correspondence loci

Definition

Let $V$ be an $n$ -dimensional vector space over the page's algebraically closed field $k$ , with $n \geq 1$ . For $0 \leq r \leq n$ , the point--plane incidence correspondence locus is the subset of the now-constructed projective product $I_{1, r} (V) = {([v], S) \in P (V) \times Gr (r, V) : v \in S},$ with its two projections. More generally, for $0 \leq a \leq b \leq n$ , the containment correspondence is $I_{a, b} (V) = {(A, B) \in Gr (a, V) \times Gr (b, V) : A \subseteq B} .$ The following lemma proves that these subsets are closed; the word "variety" is reserved until irreducibility has also been established.

Depends on

Used by

The standard incidence locus is closed Lemma

Dependency tree · two levels

14 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, §§5g and 6m (standard reference, not scraped)