Abstract
Let M be a complex manifold of dimension m and let Ψ: E → M be a complex vector bundle over M with fiber dimension q. Relative to a covering {U, V,…} of M let gUV be the transition functions of E. The bundle is called holomorphic if all these functions gUV are holomorphic (i.e., gUV, considered as a non-singular (q×q)-matrix, is a matrix of holomorphic functions in U ∩ V). If q = 1, E is called a holomorphic line bundle.
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© 1979 S.-s. Chern
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Chern, Ss. (1979). Holomorphic Vector Bundles and Line Bundles. In: Complex Manifolds without Potential Theory. Universitext. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-9344-3_6
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DOI: https://doi.org/10.1007/978-1-4684-9344-3_6
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-90422-1
Online ISBN: 978-1-4684-9344-3
eBook Packages: Springer Book Archive