DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedverified 2026-09-26 (gpt-6-sol)

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.

The Segre point map from two projective spaces

Definition

Before a categorical product has been constructed, use $\times_{s e t}$ for the Cartesian product of point sets. For the lexicographic ordering of pairs $(i, j)$ , define the Segre point map $σ_{m, n} : P_{k}^{m} \times_{s e t} P_{k}^{n} ⟶ P_{k}^{(m + 1) (n + 1) - 1}, ([x_{0} : \dots : x_{m}], [y_{0} : \dots : y_{n}]) ⟼ [x_{i} y_{j}]_{i, j} .$ The coordinate functions are bihomogeneous of bidegree $(1, 1)$ ; this convention fixes both their order and the target coordinates.

Depends on

projective space points

Used by

Dependency tree · one level

1 result within one dependency step 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, The Segre map, §6i (standard reference, not scraped)