All Questions
Tagged with toric-varieties vector-bundles
6
questions
2
votes
0
answers
133
views
Cohomology of equivariant toric vector bundles using Klyachko's filtration
I am trying to understand Klyachko's following description of the cohomology groups of locally free (hopefully more generally of reflexive) sheaves on toric varieties.
Whereas detailed literature ...
5
votes
0
answers
283
views
Non-trivial line bundle on $\mathbb{C}^{\ast} \times \mathbb{C}^{\ast}$
A line bundle is a holomorphic complex-dimension-one bundle on a complex manifold.
The complex manifold $X = \mathbb{C}^{\ast} \times \mathbb{C}^{\ast}$ admits a non-trivial line bundle for the ...
1
vote
2
answers
420
views
Embedding of a blow-up
In $\mathbb{P}^1\times\mathbb{P}^2$ take a general divisor $X$ of type $(0,2)$. Consider two general divisors $H_1,H_2$ of type $(2,1)$ and set $Y = X\cap H_1\cap H_2$.
Let $Z$ be the blow-up of $X$ ...
5
votes
0
answers
224
views
When is vector bundle over toric variety a toric variety?
Is it true that a vector bundle over a toric variety is also a toric variety if and only if it splits? if so, how do we prove it?
This seems to be the content of a remark in Oda's Tata's lectures on ...
5
votes
0
answers
161
views
Principal $G$-bundles on affine toric varieties
Let $X_\sigma$ be an affine toric variety for an action of a torus $T$ and let $\mathcal{P}$ be a toric principal $G$-bundle over $X_\sigma$ where $G$ is an affine algebraic group (here base field $k$ ...
11
votes
0
answers
675
views
Big tangent bundle
Let $X$ be a nonsingular complex algebraic variety whose tangent bundle is $T_X$. I use Lazarsfeld's book for the definition of a big vector bundle. A line bundle $L$ is big if it has Itaka dimension ...