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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.

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Reference request: Moduli spaces of bundles over singular curves

Reference: Cyril D'souza PHD thesis.(1974). Tata Institute of fundamental research,Mumbai. This thesis is concerned with constructing a "natural compactifiction" for the generalised jacobian of a sin …
61 votes
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What are some open problems in algebraic geometry?

What are the open big problems in algebraic geometry and vector bundles? More specifically, I would like to know what are interesting problems related to moduli spaces of vector bundles over projecti …