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.

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The Grassmannian of r-dimensional subspaces of a finite-dimensional vector space

Definition

Let $V$ be an $n$ -dimensional vector space over $k$ . For $0 \leq r \leq n$ , $Gr (r, V)$ denotes the parameter set of $r$ -dimensional linear subspaces of $V$ . Thus $Gr (0, V) = {0}$ and $Gr (n, V) = {V}$ . For $r < 0$ or $r > n$ we set $Gr (r, V) = \emptyset$ .

Depends on

Used by

Incidence correspondence loci Definition
Plucker coordinates and the Plucker map Definition
The boundary Grassmannians Gr(0,V) and Gr(dim V,V) Example
Standard affine charts on the Grassmannian 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)