The Picard functor for curves and their Jacobians

  • Günter Harder


In the last chapter of volume I we constructed the Jacobian of a compact Riemann surface S. The Jacobian was defined as the group of isomorphism classes of holomorphic line bundles on S. Our main result asserted that the Jacobian had the structure of a complex torus, and assuming theorems of Lefschetz and Chow we proved that this torus is a projective algebraic variety. We heavily relied on transcendental methods.


Line Bundle Cohomology Group Galois Group Abelian Variety Group Scheme 
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Copyright information

© Vieweg+Teubner Verlag | Springer Fachmedien Wiesbaden GmbH 2011

Authors and Affiliations

  • Günter Harder
    • 1
  1. 1.Max-Planck-Institute for MathematicsBonnGermany

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