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

Plucker coordinates and the Plucker map

Definition

For $S \in Gr (r, V)$ with ordered basis $(v_{1}, \dots, v_{r})$ , its Plucker point is $pl (S) = [v_{1} \land \dots \land v_{r}] \in P (Λ^{r} V) .$ After choosing an ordered basis $(e_{1}, \dots, e_{n})$ of $V$ , write this wedge in the ordered basis $(e_{i_{1}} \land \dots \land e_{i_{r}})_{i_{1} < \dots < i_{r}}$ ; its coefficients are the Plucker coordinates. Replacing the basis of $S$ multiplies the wedge by its nonzero determinant and hence does not change the projective class.

Depends on

Dependency tree · 2 levels

Sources

J. S. Milne, Algebraic Geometry, Remark 6.34