All Questions
Tagged with flag-varieties vector-bundles
9 questions
0
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113
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$\mathbb P^1$-bundle on a partial flag variety
Let $X$ be the partial flag variety of flags $0 \subset V_k \subset V_{k+2} \subset V$ where $V$ is a fixed vector space of dimension $n$ and ${\rm dim} V_k = k$ and ${\rm dim} V_{k+2} = k+2$. Is it ...
- 2,964
2
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1
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129
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Isomorphism between $\operatorname{End}_0(E)$ and $\operatorname{End}_0(E')$ as Lie algebra bundles
This may be a stupid question.
I'm reading the paper "Automorphisms of moduli spaces of vector bundles over a curve" of Indranil Biswas, Tomas L. Gomez, V. Munoz (arXiv link). I have a ...
- 297
4
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2
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955
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Borel--Bott--Weil for the Grassmannians
The Borel--Bott--Weil Theorem is usually stated for the complete flag manifold of $SU(N)$. Does an analogue hold for the other flags, for example the Grassmannians?
More precisely, suppose $G(\mathbf ...
- 449
1
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1
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774
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Geometric interpretation of Chern classes over flag manifolds
I would like to find that Chern classes of the tautological bundles over a flag manifold are dual to some cells in homology, analogously to what happens for the Grassmanian case. I have not been able ...
- 363
1
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1
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300
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Tensoring by Line Bundles to Produce Holomorphic Sections
Inspired by the line bundle case, I have the following question:
Given an equivariant holomorphic vector bundle over complex projective space, is it true that tensoring it by line bundles often ...
- 357
3
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2
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325
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Why is $\mathbb{P}(T\mathbb{P}^2)$ isomorphic to the space of complete flags $GL_3/B$?
In one the the answers to this thread " Can one embedd the projectivezed tangent space of CP^2 in a projective space? " it was mentioned that " $\mathbb{P}(T\mathbb{P}^2)$ isomorphic to the variety ...
- 131
1
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1
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201
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Non-equivariant vector bundles over complex projective $N$-space
From Grothendieck's lemma, we know that all holomorphic vector bundles over the complex projective line are direct sums of line bundles, and so, are $SU(2)$-equivariant.
I wonder, do there exist non-...
- 357
1
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1
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686
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Computing relative Lie algebra cohomology (as appears in Borel-Weil-Bott theorem)
Suppose $G$ is a complex Lie group, $P$ a Borel subgroup, $E$ a representation of $P$ that induces a vector bundle ${\cal E}$ over $G/P$. The general version of Borel-Weil-Bott theorem, as stated in ...
- 131
2
votes
2
answers
613
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Are all Equivariant Bundles of a Total Flag Manifold Constructable from Line Bundles?
As we all know, for any homogeneous space $G/H$ we have that the equivariant vector bundles over $G/H$ are characterized by the representations of $H$. Thus, for the the complex projective line $CP^1 \...
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