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Results tagged with vector-bundles
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user 450
A continuously varying family of vector spaces of the same dimension over a topological space. If the vector spaces are one-dimensional, the term line bundle is used and has the associated tag line-bundles.
32
votes
Using linear algebra to classify vector bundles over ℙ¹
Dear Ila, the linear algebra result you mention is due to Dedekind-Weber and was published in Crelle's Journal dated 1882, in their article "Theorie der algebraischen Funktionen einer Veränderlichen …
- 47.5k
17
votes
Accepted
Existence of non-split vector bundles on smooth projective varieties
Yes, it is true that (over an algebraically closed field) the only positive-dimensional smooth projective variety on which every algebraic vector bundle splits as a sum of line bundles is $\mathbb P^ …
- 47.5k
15
votes
Reference request: moduli spaces of vector bundles
Dear Mohammad, there is a rather elementary book Introduction to Moduli Problems and Orbit spaces by P.E. Newstead which will explain to you why stability is important, give you lots of examples (Ch …
- 47.5k
14
votes
Accepted
Recommended books/lecture notes for vector bundle on algebraic curve
The modern theory of vector bundles over a curve starts with Grothendieck's article Sur la classification des fibrés holomorphes sur la sphère de
Riemann. American Journal of Mathematics, 79, 121–138, …
- 47.5k
5
votes
Is analytic Quillen-Suslin simple?
Dear David, I think there might be a slightly simpler proof of the analytic Quillen-Suslin theorem.
Given a holomorphic vector bundle $E$ on $\mathbb C^n$, it has a holomorphic connection since its A …
- 47.5k