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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.

3 votes
0 answers
158 views

Semistability of restrictions of a semistable vector bundle over a reducible nodal curve

Let $C$ be a reducible nodal curve over complex numbers with two smooth components $C_1$ and $C_2$ intersecting at the only node $P$. Let $E$ be a $\omega$ semistable vector bundle over $C$ of rank $r …
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3 votes
0 answers
400 views

Some queries on Moduli Space of Parabolic Vector Bundles on curve

In "Moduli of Vector Bundles on curves with Parabolic Structures"-Bulletin of the American Mathematical Society Volume 83, Number 1, January 1977 the author announces the following result on moduli sp …
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0 votes
1 answer
225 views

Any no-zero homomorphism of holomorphic vector bundles over a compact Riemann surface factor...

I was reading the paper "Stable and Unitary vector bundles on a compact surface" by Narashiman and Seshadri. I quote from the paper- Can someone please explain how does any non-zero homomorphism o …
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