Alphabeta MathHow 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.
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These labels describe origin, not correctness: citations and verification chips remain separate evidence.
The Grassmannian of r-dimensional subspaces of a finite-dimensional vector space
Definition
Let be an -dimensional vector space over . For , denotes the parameter set of -dimensional linear subspaces of . Thus and . For or we set .
Depends on
Used by
- The Euler characteristic does not determine the signature Counterexample
- Incidence correspondence loci Definition
- Plucker coordinates and the Plucker map Definition
- Real Stiefel and Grassmann optimization conventions Definition
- The boundary Grassmannians Gr(0,V) and Gr(dim V,V) Example
- The one-loop quiver extension correspondence in dimension two Example
- Arbitrary-framing A1 varieties and their conormal Hecke correspondence Lemma
- Semistable loci of finite-quiver representations are open Lemma
- Standard affine charts on the Grassmannian Lemma
- The quiver exact-sequence correspondence is smooth and proper Lemma
- The variety of complete flags of a finite-dimensional vector space is smooth projective Lemma
Dependency tree · two levels
23 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, §6m Grassmann varieties (standard reference, not scraped)
- MIT 18.725 Algebraic Geometry, Lecture 4, Example 4 (standard reference, not scraped)