All Questions
8 questions
2
votes
1
answer
209
views
Trivial rational solution of a system of hyperplanes
Let us consider a vector space $ V $ over $ \mathbb{Q} $ of dim $6$. We denote all the two dimensional subspace in $ V $ by $ G(2,6) $ (The Grassmanian variety). One can define a map $ p $ from $ G(2,...
- 923
3
votes
0
answers
151
views
Reference request: invariants/tableaux functions for 4 lines in $P^3$
Does anybody have a reference for invariants of configurations of linear subspaces in the projective space?
In particular I would be curious to see an explicit expression of the invariant functions ...
- 3,779
1
vote
1
answer
187
views
Subbundle generated by linearly dependent sections
On $\mathbb{P}^1$ consider the trivial bundle $\mathcal{O}\oplus \mathcal{O}$, and the subbundle $\mathcal{L}_{a,b}\subset\mathcal{O}\oplus \mathcal{O}$ that on an open subset $U$ of $\mathbb{P}^1$ is ...
user68440
2
votes
1
answer
364
views
Linear subspaces in quadric hypersurfaces
Consider $H_1,H_2,H_3\subset\mathbb{P}^{2m+1}$ three general linear subspaces of projective dimension $m$.
Then there exists a quadric hypersurface $Q^{2m}\subset\mathbb{P}^{2m+1}$ containing $H_1,...
- 8,998
4
votes
2
answers
750
views
Vector bundles on Grassmannians
Let $Gr(k,n)$ be the Grassmannian of $k$-dimensional vector subspaces $H^k$ of an $n$-dimensional vector space $V$.
Let us fix an $h$-dimensional vector subspace $\Gamma\subset V$ with $h\leq k$, and ...
- 79
3
votes
1
answer
433
views
Varieties parametrizing skew-symmetric matrices
Let $V$ be a vector space of dimension $n$ and let us consider the projective space $\mathbb{P}(\bigwedge^2V)$ parametrizing skew-symmetric matrices.
Let $M\in\mathbb{P}(\bigwedge^2V)$, for any ...
user75933
2
votes
2
answers
301
views
A $d$-form on ${\mathbb R}^n$ that vanishes on $\binom{d+n-1}{n-1}$ general points, vanishes identically
I'm looking for a reference for the fact that a $d$-form on ${\mathbb R}^n$ that vanishes on $p_1,..,p_{\binom{d+n-1}{n-1}}$ general points, vanishes identically.
A specific construction of a set of ...
- 265
44
votes
2
answers
2k
views
Is this lemma in elementary linear algebra new?
Is anyone familiar with the following, or anything close to it?
Lemma. Suppose $A$, $B$ are nonzero finite-dimensional vector spaces
over an infinite field $k$, and $V$ a subspace of $A\otimes_k B$
...
- 595