Tagged Questions
3
votes
0answers
79 views
A question of extension of vector bundles.
Fix $p \in \mathbb{P}^1$. Let $X=\mathbb{P}^1\times \mathbb{P}^1$, $C_1=\mathbb{P}^1\times \{p\}$ and $C_2=\{p\}\times \mathbb{P}^1$. Since $\mathrm{Ext}^1(\mathcal{O}_{C_2},\mathcal{O}_{C_1})\cong ...
5
votes
0answers
79 views
When is the pushforward / direct image of a reflexive sheaf locally free?
I have seen a number of theorems that guarantee the direct image of a reflexive sheaf to be reflexive again, or for the direct image of a locally-free sheaf to be locally free again.
This makes me ...
4
votes
1answer
151 views
Exterior power of a tensor product
Given 2 vector bundles $E$ and $F$ of ranks $r_1, r_2$, we can define $k$'th exterior power $\wedge^k (E \otimes F)$.
Is there some simple way to decompose this into tensor products of various ...
