Holomorphic Vector Bundles and Line Bundles

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


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.


Line Bundle Holomorphic Function Meromorphic Function Complex Manifold Curvature Form 
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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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