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A continuously varying family of one-dimensional vector spaces over a topological space. A related tag is the vector-bundles tag.

3 votes
0 answers
212 views

Line bundles with meromorphic transition functions

I have the following situation: let $X$ be a projective complex manifold and let $f \in H^1(X,\mathcal{M}^{\times})$. So $f$ defines something like a line bundle with meromorphic transition functions. …
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  • 153
2 votes
0 answers
133 views

Symmetric group-cocycle descends to symmetric product

Let $C$ be a complex curve with universal covering $\tilde{C}$ (which in my case is the upper half plane). Any group-cocylce $e \in H^1(\pi_1(C^n),H^0(\tilde{C}{}^n,\mathcal{O}^{\times}))$ defines a l …
KuSi's user avatar
  • 153
0 votes
1 answer
270 views

Universal covering of symmetric product

Let $C$ be a 1-dimensional complex manifold whose universal covering is provided by the half-plane $\mathcal{H}=\{z \in \mathbb{C} \mid \operatorname{Im}z>0\}$. The symmetric product $C^{(n)} = C^n / …
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  • 153