Can somebody give me a general idea how to define a vector bundle of rank $N$ if we have a sheaf, which is locally given by $N$ holomorphic functions?
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This previous question (https://math.stackexchange.com/questions/1594069/vector-bundle-as-locally-free-coherent-sheaves) might help – Sam Freedman Jan 16 '20 at 16:42
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What does "locally given by $N$ holomorphic functions" mean? Do you know the sheaf is locally free? – Ted Shifrin Jan 16 '20 at 19:42