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Holomorphic Vector Bundles and Line Bundles

  • Shiing-shen Chern
Part of the Universitext book series (UTX)

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.

Keywords

Line Bundle Holomorphic Function Meromorphic Function Complex Manifold Curvature Form 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© S.-s. Chern 1979

Authors and Affiliations

  • Shiing-shen Chern
    • 1
  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA

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