Hello I was wondering if anybody can direct me to a paper or a book regarding the volume of $Gr(2,4) $ or generic complex Grassmanian manifolds of order $k$. My own heuristic meth …

Let $Trop(Gr(m,n))$ denote the tropicalization of the grassmannian $Gr(n,m)$. Let $\phi^m : \mathbb R^{n \choose 2} \rightarrow \mathbb R^{n \choose m}$ such that $X_{i,j} \righta …

A while ago I heard that there was no known triangulation of the Grassmannian of 3-planes in 6-space. To believe a statement like that, you have to be a little bit ungenerous abou …

The intersection of 3 quadrics in $P^5$ is a K3 surface $S$. There is a natural map $S^{[2]} \to G(1,5)$ well defined everywhere, because a generic K3 doesn't contain any line and …

Suppose I have an $n\times n$ real (or complex) matrix of rank $k$, and I want to pick $k$ linearly independent rows from it. I want to do this in a continuous fashion as the matr …

I'm trying to evaluate $$\frac{\delta}{\delta \eta(x)}e^{-\int dz \theta^*(z)\eta(z)}$$ Where $\theta^*(x)$ and $\eta(x)$ are Grassmann valued functions. The context of the functio …

Let $S$ be a noetherian scheme, $\mathcal{E}$ a quasi-coherent sheaf on $S$ and let $d \in \mathbb{N}$. There is a Plücker embedding $\omega : \mathrm{Grass}_d(\mathcal{E}) \hookri …

The Grassmann manifold $\widetilde{Gr}(k,\Bbb{R}^n)$ of oriented $k$-planes in $\Bbb{R}^n$ is a double cover of the Grassmann manifold $Gr(k,\Bbb{R}^n)$ of non-oriented $k$-planes. …

I was reading chapter 6 in the book of Harris on Algebraic geometry and came to the following puzzle. It seems to me that every Schubert cell in a Grassmanian is obtaining by cutt …

It's well known that the even-dimensional complex quadric $Q_{2n}$, defined by the equation $z_1^2+\cdots +z_{2n+2}^2=0$ in complex projective space $CP^{2n+1}$, is diffeomorphic w …

I was reading Postnikov's paper [TOTAL POSITIVITY, GRASSMANNiANS, AND NETWORKS][1] when I came across the definition of the totally nonnegative Grassmannian $Gr_{kn}^{tnn} \subset …

This works over the reals but not over the complex field. Consider the set of all $n\times n$ matrices $A$ such that 1. $A^2=A$ 2.$A^T=A$ 3. $\mathrm{Trace}(A)=1$ The first condit …

I want to learn more about orthogonal and lagrangian (or symplectic) grassmannians. What are good references?

Let $G(k,n)$ be the Grassmannian of complex $k$-planes in $\mathbb{C}^n$. Then for $k_1+k_2=k$ and $n_1+n_2=n$, $G(k_1,n_1)\times G(k_2,n_2)$ is a submanifold of $G(k,n)$. So the c …

I'm looking for something like a Grassmannian, but which parameterizes the submodules of a module rather than the subspaces of a vector space. Most specifically, I'm looking for so …