# Tagged Questions

Grassmannians are algebraic varieties whose points corresponds to vector subspaces of a fixed dimension in a fixed vector space.

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### Reference quest: variety of lines and variety of planes

Let $X\subset \mathbb P_{\mathbb C}^n$ be a smooth projective variety, $F(X)\subset G(2,n+1)$ its Fano variety of lines and $$I_F=\left\{([l],[l'])\in F(X)\times F(X), l\cap l'\neq \emptyset\right\}$$ ...
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### Schubert calculus and Pieri's formula

In the lecture notes Grassmannians: the first example of a moduli space. MIT Open Course Ware. page 7: Are there any formal publications (books/papers) where I can find the formula?
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### Steenrod operations on cohomology of grassmannians

Let $G_k(\mathbb{R}^n)$, $n\geq k$ and $G_k(\mathbb{R}^\infty)$ be the finite-dimensional and infinite-dimensional grassmannians respectively. Their cohomology rings are expressed in terms of ...
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### (The Homotopy type of the) lifting of homeomorphism of Grassmanian

For $k<n$ put $FM_{k\times n}$ for the space of all $k\times n$ full rank matrices with real or complex entries. Note that the permutation group $S_{n}$ has an obvious action on this space ...
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I've heard about the followign result: for each two natural numbers $d,n \in \mathbb{N}$ one can find a number $k \in \mathbb{N}$ with the following property: for each CW-complex $X$ with $\dim X \leq ... 7answers 2k views ### Conceptual algebraic proof that Grassmannian is closed in Plucker embedding I'm planning lectures for my intro algebraic geometry course, and I noted something awkward that is coming up. We're starting projective varieties soon. Of course, we'll prove that projective maps are ... 2answers 481 views ### Plucker embedding and tautological/universal quotient bundle Let$G$be a Grassmannian and$Q$the tautological/universal quotient bundle of$G$. As far as I understand, the associated tautological quotient line bundle for the Plucker embedding of the ... 1answer 132 views ### Rational normal curves on Grassmanians Consider the Grassmanian$G(k,n)$($k\le \frac{n}{2}$) and take its Plucker embedding. Consider now the space of all normal rational curves of degree$k$, contained in the Plucker embedding of the ... 1answer 342 views ### Is the Lie quadric$Q^3$isomorphic to the Lagrangian Grassmannian$LG(2,4)$? On the paper http://arxiv.org/abs/1009.1364 (published on Proc. London Math. Soc.) I've found an interesting statement: The Lie quadric$Q^3$, i.e., the space of all points, lines and circles ... 1answer 508 views ### Two questions about the grassmannian There are two statements about the grassmannian (of complex k-planes in n-space embedded via Plucker coordinates) that I have encountered in several places never accompanied with a proof or reference. ... 2answers 217 views ### Curve of 3-secant lines Let$C\subset\mathbb{P}^{3}$be a smooth, non-degenerate curve over an algebraically closed field of characteristic zero. Let$d$be the degree of$C$and$g$be its genus. Consider the variety$S_{3}...
I am new to the Grassmannian. I have read about Grassmannian frames in $\mathbb R^n$. My question is can we define Grassmannian frames in a Grassmannian space $Gr(k,n)$ just like in $\mathbb R^n$? ...
Let $Gr(c,\infty)$ be the complex grassmannian of $c$-dimensional subspaces of the infinite dimensional complex space. Every finite dimensional grassmannian, $Gr(c,N)$, can be thought as a subspace of ...