# Questions tagged [grassmannian]

In mathematics, the Grassmannian $\mathbf{Gr}(r, V)$ is a space which parameterizes all linear subspaces of a vector space $V$ of given dimension $r$.

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### Incidence correspondence of Grassmannian is a projective variety

I'm working the following question: Let $$\Sigma = \{(L, p) \in G(k,n) \times \mathbb{P}^{n-1} \mid L\subset \mathbb{P}^{n-1}, p \in L\}.$$ Here we're viewing $G(k,n)$ as $(k-1)$-dimensional ...
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### Prove a “distance” is a metric between vector spaces

In a paper by Alan Edelman, "The geometry of algorithms with orthogonality constraints" (page 35 ), there are several definitions to the notation "distance" between vector spaces on the Grassmanian. ...
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### Reference for Grassmannian Manifold

I need to study Grassmannian manifold in a good way, like study vector bundles, tangent bundle,... and etc on Grassmannian manifold. I found some lecture and books but they were written an ...
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### How can I get the matrix form for a schubert cell?

I am trying to learn how to understand the cell-decomposition for the grassmannian and am following these notes: http://www.math.drexel.edu/~jblasiak/grassmannian.pdf. On page 2 the author considers ...
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### Intersection of Schubert cycles

I want to compute intersection of the Schubert cell $\sigma_{(3,0)}$ with all the cells $\sigma_{a_1, a_2}$ in the grassmanian $G(2,5)$. I am not sure I am doing correctly but I can't see my mistake. ...
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### Understanding the cohomology ring of the Grassmannian

Some background first: I'm trying to understand the solution of some enumerative geometry problems, such as proving that a smooth cubic contains $27$ lines. I know that this becomes easier once one ...
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Let $V$ be a vector space, then denote the simple or decomposable $m$-vectors in $\bigwedge^m V$ by $GC_m(V)$. I am struggling to understand the topology of the bundle $GC_m(TN) = \bigsqcup_{q\in N} ... 1answer 55 views ### Ref. Request — Tautological Bundle over$G_{k,n}(\mathbb{R})$I'm interested right now to learn more about the tautological bundle over the Grassmann manifold$G_{k,n}(\mathbb{R})$, but I'm currently having trouble finding the appropriate texts to check out. ... 0answers 76 views ### Chern classes of hyper-Kähler fourfolds in Grassmannians Both the Fano variety$F$of lines in a general cubic fourfold and the "Debarre–Voisin" fourfolds$Y_\sigma$introduce in [DV] are smooth, four-dimensional, hyper-Kähler subvarieties of Grassmannians (... 1answer 389 views ### What are the first 8 homotopy groups of the complex Grassmannian$G_\mathbb{C}(2,4)$? I was trying to find any information about the first couple of homotopy groups of the complex Grassmannian$G_\mathbb{C} (2,4)$of complex planes in complex$4$-space. I need the first seven or eight ... 2answers 655 views ### Sub Matrix of an Orthogonal Matrix is always singular? I am trying to implement Grassmanian rank one update (GROUSE) as per this paper . For the solution of the least squares problem of (1) in the paper the value of$w$is$w$=$(U_{\Omega_{t}}^TU_{\...
I am trying to understand what is a Grassmannian. Starting with the projective space $\mathbb{R}P^n$ = {lines in $\mathbb{R}^{n+1}$} and the grassmannian $G_r(k,n)$ = {\$k-dimentional\space subspace\...